Large Designs: lambda, v, t, k


Lehrstuhl II für Mathematik

Universität Bayreuth
D-95440 Bayreuth

Anton Betten
Reinhard Laue
Alfred Wassermann

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creation date: Thu Mar 11 15:29:58 MET 1999

WARNING: Completeness of know results is attempted only for t >= 6 and v <= 40 in the following list.


298 5-(12,6,1) (complement has $\lambda=6$)
Alltop construction for design number 295
$Aut(Icosahedron)$ complementary design:5-(12,6,6) with #blocks = #5-subsets = 792
\cite{Witt38} $M_{12}$ (1 isom. type)

2750 5-(24,6,1) (complement has $\lambda=18$)
\cite{Denniston76} $PSL(2,23)$ (3 isom. types)

2888 5-(24,8,1) (complement has $\lambda=968$)
\cite{Witt38} $M_{24}$ 1 isomorphism type

4354 5-(28,7,1) (complement has $\lambda=252$)
Steiner system ! $PGL(2,27)$ (1 isom. type) \cite{Denniston76}

5282 5-(36,6,1) (complement has $\lambda=30$)
\cite{Bettenetal98a} $PGL(2,17)\times C_2$

5399 5-(48,6,1) (complement has $\lambda=42$)
\cite{Denniston76} \cite{Grannelletal93} $PSL(2,47)$ (459 isom. types)

5516 5-(72,6,1) (complement has $\lambda=66$)
\cite{Mills78}\cite{Grannelletal98} $PSL(2,71)$ short orbits: 4204 isomorphism types
\cite{Mills78}\cite{Grannelletal98} $PSL(2,71)$ short orbits: 4204 isomorphism types, 916299 isomorphism types \cite{BettenMolodtsovLaueWassermann98}

5520 5-(84,6,1) (complement has $\lambda=78$)
\cite{Denniston76} $PSL(2,83)$ 38717 isomorphism types from short orbits \cite{Grannelletal98}
\cite{Denniston76} $PSL(2,83)$ 38717 isomorphism types from short orbits \cite{Grannelletal98}, semiregular: 3 isomorphism types \cite{BettenMolodtsovLaueWassermann98}

868 5-(108,6,1) (complement has $\lambda=102$)
\cite{Mathon97} $PSL(2,107)$ >= 1000 isomorphism types

882 5-(132,6,1) (complement has $\lambda=126$)
\cite{Mathon97} $PSL(2,131)$ >= 100 isomorphism types

911 5-(168,6,1) (complement has $\lambda=162$)
\cite{Mathon97} $PSL(2,167)$ >= 4 isomorphism types

11666 5-(244,6,1) (complement has $\lambda=238$)
$P\Sigma_L(2,3^5)$ \cite{BettenMolodtsovLaueWassermann98} >= 303 isomorphism types

302 5-(12,6,2) (complement has $\lambda=5$)
Alltop construction for design number 299
$Aut(Icosahedron)$, $PGL(2,11)$ supplementary design has same parameters
Alltop construction

2754 5-(24,6,2) (complement has $\lambda=17$)
$PGL(2,11)\times C_2$ 1 isomorphism type, $PSL(2,11)\times C_2$ 611 solutions
$PGL(2,23)$ 6 isomorphism types, $PSL(2,23)$ 38 isomorphism types

2892 5-(24,8,2) (complement has $\lambda=967$)
\cite{KramerMagliveras74}
\cite{AssmusMattson66a} $PGL(2,23))$

4338 5-(28,6,2) (complement has $\lambda=21$)
$PGL(2,13)\times C_2$ 11 solutions
$PSL(2,27)$ (62 isom. types) \cite{KreherRadziszowski87a}

5306 5-(36,6,2) (complement has $\lambda=29$)
$PGL(2,17)\times C_2$

5415 5-(48,6,2) (complement has $\lambda=41$)
$PGL(2,23)\times C_2$, $PSL(2,47)$

5456 5-(52,6,2) (complement has $\lambda=45$)
$P\Gamma L(2,25)\times C_2$ many solutions

11670 5-(244,6,2) (complement has $\lambda=237$)
$P\Sigma_L(2,3^5)$ \cite{BettenMolodtsovLaueWassermann98}

306 5-(12,6,3) (complement has $\lambda=4$)
Alltop construction for design number 303
Alltop construction

886 5-(14,6,3) (complement has $\lambda=6$)
Brouwer 1977/1986

896 5-(16,6,3) (complement has $\lambda=8$)
Brouwer 1977/1986

2758 5-(24,6,3) (complement has $\lambda=16$)
\cite{AssmusMattson69} $M_24$ 1 isomorphism type
$PGL(2,23)$ 3 isomorphism types

2808 5-(24,7,3) (complement has $\lambda=168$)
\cite{Driessen78} $M_{24}$

2896 5-(24,8,3) (complement has $\lambda=966$)
\cite{KramerMagliveras74}
\cite{KramerMagliveras74}

4342 5-(28,6,3) (complement has $\lambda=20$)
$PSL(2,27)$ \cite{KreherRadziszowski87a}

5310 5-(36,6,3) (complement has $\lambda=28$)
$PGL(2,17)\times C_2$

5427 5-(48,6,3) (complement has $\lambda=40$)
$PGL(2,23)\times C_2$, $PSL(2,47)$

74 5-(64,6,3) (complement has $\lambda=56$)
$A\Gamma L(2,8)$ 190 isomorphism types

872 5-(13,6,4) (selfcomplementary)
\cite{Kreher86a}
derived from number 878
derived from complement of number 878

878 6-(14,7,4) (selfcomplementary)
Alltop construction for design number 872
$C_{13}+$ (2 isom. types) \cite{KreherRadziszowski86}, Halving of the complete design

947 5-(18,6,4) (complement has $\lambda=9$)
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
derived from number 5524

1416 5-(19,6,4) (complement has $\lambda=10$)
$Hol(C_{19})$ (255 isom. types) \cite{Bettenetal98b}

5524 6-(19,7,4) (complement has $\lambda=9$)
$Hol(C_{17})++$ (1 isom. type) \cite{Bettenetal97b}

1877 5-(21,6,4) (complement has $\lambda=12$)
$Hol(C_{21})$

7850 5-(22,6,4) (complement has $\lambda=13$)
derived from number 7848

7848 6-(23,7,4) (complement has $\lambda=13$)
derived from number 7847

2762 5-(24,6,4) (complement has $\lambda=15$)
$PGL(2,23)$ 18 isomorphism types
$PGL(2,11)\times C_2$ 392 solutions

2900 5-(24,8,4) (complement has $\lambda=965$)
\cite{KramerMagliveras74}
\cite{KramerMagliveras74}

7847 7-(24,8,4) (complement has $\lambda=13$)
PSL(2,23) (1 isom. type) \cite{Bettenetal98b}

72 5-(27,6,4) (complement has $\lambda=18$)
$ASL(3,3)^{13}$ NOT SIMPLE! 1 orbit twice

4346 5-(28,6,4) (complement has $\lambda=19$)
$PSL(2,27)$ \cite{KreherRadziszowski87a}

5314 5-(36,6,4) (complement has $\lambda=27$)
$PGL(2,17)\times C_2$

5431 5-(48,6,4) (complement has $\lambda=39$)
$PGL(2,23)\times C_2$, $PSL(2,47)$

900 5-(16,6,5) (complement has $\lambda=6$)
Brouwer 1977/1986

951 5-(18,6,5) (complement has $\lambda=8$)
\cite{Brouwer86}

7857 5-(22,6,5) (complement has $\lambda=12$)
derived from number 7855

7855 6-(23,7,5) (complement has $\lambda=12$)
derived from number 7854

2766 5-(24,6,5) (complement has $\lambda=14$)
$PGL(2,23)$ 13 isomorphism types
$PGL(2,11)\times C_2$ 10118 solutions

2904 5-(24,8,5) (complement has $\lambda=964$)
\cite{KramerMagliveras74}
\cite{KramerMagliveras74}

7854 7-(24,8,5) (complement has $\lambda=12$)
PSL(2,23) (138 isom. types) \cite{Bettenetal98b}

50 5-(28,6,5) (complement has $\lambda=18$)
$PSU(3,9)$ 5724 isomorphism types
$PSL(2,27)$ \cite{KreherRadziszowski87a}

4866 5-(30,6,5) (complement has $\lambda=20$)
$\lambda=5$ $PSL(2,29)$ has 192 solutions (17 isom. types), $PGL(2,29)$ has 158 solutions (=158 isom. types)
\cite{Kreher95}

5261 5-(34,6,5) (complement has $\lambda=24$)
\cite{Sebille98} $P\Gamma L(2,16)\times C_2$ 15 solutions

5318 5-(36,6,5) (complement has $\lambda=26$)
$PGL(2,17)\times C_2$

5435 5-(48,6,5) (complement has $\lambda=38$)
$PGL(2,23)\times C_2$, $PSL(2,47)$

5526 5-(18,6,6) (complement has $\lambda=7$)
derived from number 5525

973 5-(18,7,6) (complement has $\lambda=72$)
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type, block-transitive

1159 5-(18,8,6) (complement has $\lambda=280$)
$PGL(2,16)+$ 1 isomorphism type
\cite{MacWilliams78}

1420 5-(19,6,6) (complement has $\lambda=8$)
$Hol(C_{19})$ (17193 isom. types) #blocks = #5-subsets \cite{Bettenetal98b}

5525 6-(19,7,6) (complement has $\lambda=7$)
$Hol(C_{19})$ (3 isom. types) \cite{Bettenetal97b}

7862 5-(22,6,6) (complement has $\lambda=11$)
derived from number 7860
$Hol(C_{19})+++$

11052 5-(23,6,6) (complement has $\lambda=12$)
$Hol(C_{23})$ >=2 solutions

7860 6-(23,7,6) (complement has $\lambda=11$)
derived from number 7859

2770 5-(24,6,6) (complement has $\lambda=13$)
$PGL(2,23)$ 24 isomorphism types
$PGL(2,11)\times C_2$
derived from number 8000

2849 5-(24,7,6) (complement has $\lambda=165$)
\cite{Kreheretal90} $PGL(2,23))$

2908 5-(24,8,6) (complement has $\lambda=963$)
\cite{KramerMagliveras74}
\cite{KramerMagliveras74}

3642 5-(24,9,6) (complement has $\lambda=3870$)
\cite{AssmusMattson69c} $PSL(2,23)$ (1 isomorphism type) block transitive

7859 7-(24,8,6) (complement has $\lambda=11$)
PSL(2,23) (>= 132 isom. types) \cite{Bettenetal98b}

8000 6-(25,7,6) (complement has $\lambda=13$)
derived from number 7999

7999 7-(26,8,6) (complement has $\lambda=13$)
PGL(2,25) (14 solutions, 7 isom. types) \cite{Bettenetal98b}

45 5-(27,6,6) (complement has $\lambda=16$)
derived from number 44

54 5-(28,6,6) (complement has $\lambda=17$)
$PSU(3,9)$ 5290 isomorphism types
$PSL(2,27)$ \cite{KreherRadziszowski87a}

44 6-(28,7,6) (complement has $\lambda=16$)
$PSU(3,9)$ $\ge $ 10 isomorphism types

7655 5-(31,6,6) (complement has $\lambda=20$)
derived from number 7653

7653 6-(32,7,6) (complement has $\lambda=20$)
$PSL(2,31)$ (>=18) \cite{Bettenetal97b}

5322 5-(36,6,6) (complement has $\lambda=25$)
$PGL(2,17)\times C_2$

5439 5-(48,6,6) (complement has $\lambda=37$)
$PGL(2,23)\times C_2$, $PSL(2,47)$

7869 5-(22,6,7) (complement has $\lambda=10$)
derived from number 7867

7867 6-(23,7,7) (complement has $\lambda=10$)
derived from number 7866

2774 5-(24,6,7) (complement has $\lambda=12$)
$PGL(2,23)$ 20 isomorphism types
$PGL(2,11)\times C_2$

2912 5-(24,8,7) (complement has $\lambda=962$)
\cite{KramerMagliveras74}
\cite{KramerMagliveras74}

7866 7-(24,8,7) (complement has $\lambda=10$)
PSL(2,23) (>= 126 isom. types) \cite{Bettenetal98b}

4350 5-(28,6,7) (complement has $\lambda=16$)
$PSL(2,27)$ \cite{KreherRadziszowski87a}

4389 5-(28,7,7) (complement has $\lambda=246$)
$PSL(2,27)$ (2 isom. types)

5326 5-(36,6,7) (complement has $\lambda=24$)
$PGL(2,17)\times C_2$

5443 5-(48,6,7) (complement has $\lambda=36$)
$PGL(2,23)\times C_2$, $PSL(2,47)$

5554 5-(21,6,8) (selfcomplementary)
derived from number 5553
derived from complement of number 5553

7876 5-(22,6,8) (complement has $\lambda=9$)
derived from number 7874

5553 6-(22,7,8) (selfcomplementary)
(6-(8m+6,7,4m) for m=2 \cite{Teirlinck89}), Halving of the complete design

7874 6-(23,7,8) (complement has $\lambda=9$)
derived from number 7873

2778 5-(24,6,8) (complement has $\lambda=11$)
$PGL(2,23)$ 51 isomorphism types

2916 5-(24,8,8) (complement has $\lambda=961$)
\cite{KramerMagliveras74}
\cite{KramerMagliveras74}

7873 7-(24,8,8) (complement has $\lambda=9$)
PSL(2,23) (>= 63 isom. types) PGL(2,23) (4 isom. types) #blocks = #7-subsets \cite{Bettenetal98b}, \cite{Bettenetal97b}

58 5-(28,6,8) (complement has $\lambda=15$)
$PSU(3,9)$ many isomorphism types
$PSL(2,27)$ \cite{KreherRadziszowski87a}

4393 5-(28,7,8) (complement has $\lambda=245$)
$PSL(2,27)$ (2 isom. types)

5330 5-(36,6,8) (complement has $\lambda=23$)
$PGL(2,17)\times C_2$

5447 5-(48,6,8) (complement has $\lambda=35$)
$PSL(2,47)$

2782 5-(24,6,9) (complement has $\lambda=10$)
$PGL(2,23)$ 43 isomorphism types
$PGL(2,11)\times C_2$

2885 5-(24,7,9) (complement has $\lambda=162$)
\cite{Kreheretal90} $PGL(2,23))$

2920 5-(24,8,9) (complement has $\lambda=960$)
\cite{KramerMagliveras74}
\cite{KramerMagliveras74}

62 5-(28,6,9) (complement has $\lambda=14$)
$PSU(3,9)$ many isomorphism types
$PSL(2,27)$ \cite{KreherRadziszowski87a}

5334 5-(36,6,9) (complement has $\lambda=22$)
$PGL(2,17)\times C_2$

5347 5-(38,6,9) (complement has $\lambda=24$)
\cite{Sebille98} $PGL(2,37)$

3847 5-(25,7,10) (complement has $\lambda=180$)
TvT: 5-(24,6,1) $\cup$ 5-(24,7,9)

4334 5-(28,6,10) (complement has $\lambda=13$)
$PSL(2,27)$ \cite{KreherRadziszowski87a}

9422 5-(31,6,10) (complement has $\lambda=16$)
derived from number 9418

9418 6-(32,7,10) (complement has $\lambda=16$)
derived from number 9416

9416 7-(33,8,10) (complement has $\lambda=16$)
$P\Gamma L(2,32)$ (4996426 isom. types) \cite{Bettenetal95b}

5286 5-(36,6,10) (complement has $\lambda=21$)
$PGL(2,17)\times C_2$

66 5-(28,6,11) (complement has $\lambda=12$)
$PSU(3,9)$ many isomorphism types
$PSL(2,27)$ \cite{KreherRadziszowski87a}

5290 5-(36,6,11) (complement has $\lambda=20$)
$PGL(2,17)\times C_2$

78 5-(64,6,11) (complement has $\lambda=48$)
$ASL(3,4)$ 8 isomorphism types
$ASL(3,4)$ 48 solutions, 18 isomorphism types
$ASL(3,4)$ 48 solutions

892 5-(14,7,12) (complement has $\lambda=24$)
Alltop construction for design number 889
$C_4xId_3$ (halving of the complete design),Alltop from 4-(13,6,12)
$LS[3](5,7,14)$ Alltop-extension $LS[3](4,6,13)$
Alltop construction from 4-(13,6,12), 8 solutions, res(6-(15,7,3))

915 5-(17,7,12) (complement has $\lambda=54$)
Brouwer 1977/1986

955 5-(18,7,12) (complement has $\lambda=66$)
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

2786 5-(24,7,12) (complement has $\lambda=159$)
\cite{Kreheretal90}

3294 5-(24,9,12) (complement has $\lambda=3864$)
$PGL(2,23)$ (1 isomorphism type) block transitive

7543 5-(29,6,12) (selfcomplementary)
derived from number 7541
derived from complement of number 7541

7541 6-(30,7,12) (selfcomplementary)
$PSL(2,29)$ (many) (6-(8m+6,7,4m) for m=3 (\cite{Teirlinck89})), Halving of the complete design

5214 5-(33,6,12) (complement has $\lambda=16$)
\cite{Sebille98} $P\Gamma L(2,32)$

5257 5-(34,6,12) (complement has $\lambda=17$)
\cite{Sebille98} $P\Gamma L(2,16)\times C_2$ 15 solutions

5294 5-(36,6,12) (complement has $\lambda=19$)
$PGL(2,17)\times C_2$

5343 5-(38,6,12) (complement has $\lambda=21$)
\cite{Sebille98} $PGL(2,37)$

5403 5-(48,6,13) (complement has $\lambda=30$)
$PSL(2,47)$

873 5-(13,7,14) (selfcomplementary)
supplementary design of number 872
residual design of number 878
residual design of complement of number 878

1056 5-(18,8,14) (complement has $\lambda=272$)
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

5298 5-(36,6,14) (complement has $\lambda=17$)
$PGL(2,17)\times C_2$

893 5-(15,7,15) (complement has $\lambda=30$)
TvT: 5-(14,6,3) $\cup$ 5-(14,7,12) \cite{TranvanTrung86}

904 5-(16,7,15) (complement has $\lambda=40$)
$A_4\times D_4$ 42 solutions
Brouwer 1977/1986

1165 5-(18,9,15) (complement has $\lambda=700$)
Alltop construction for design number 1162
\cite{Brouwer86} Alltop(res(5-(18,8,6))
\cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type

2790 5-(24,7,15) (complement has $\lambda=156$)
\cite{Kreheretal90}

3875 5-(25,9,15) (complement has $\lambda=4830$)
TvT: 5-(24,8,3) $\cup$ 5-(24,9,12)

4362 5-(28,7,15) (complement has $\lambda=238$)
$PSL(2,27)$ (>=1 isom. types)

5302 5-(36,6,15) (complement has $\lambda=16$)
$PGL(2,17)\times C_2$

1077 5-(18,8,16) (complement has $\lambda=270$)
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type, block-transitive

1899 5-(22,7,16) (complement has $\lambda=120$)
\cite{Kreher95} $PSL(2,19)++$ 9 solutions
\cite{Kreher95} $PGL(2,19)++$

2979 5-(24,8,16) (complement has $\lambda=953$)
$PSL(2,23)$ 2 isomorphism types

7723 5-(37,6,16) (selfcomplementary)
derived from number 7721
derived from complement of number 7721

7721 6-(38,7,16) (selfcomplementary)
\cite{Ajoodani94} using 6_(22,7,7)

2995 5-(24,8,17) (complement has $\lambda=952$)
$PSL(2,23)$ 4 isomorphism types

5407 5-(48,6,17) (complement has $\lambda=26$)
$PSL(2,47)$

877 5-(14,7,18) (selfcomplementary)
Tran van Trung construction with supplementary design for design number 872
Alltop construction for design number 874
design of number 878 with respect to smaller t
complementary design of number 878 with respect to smaller t
$LS[2](5,7,14)$ $C_{13}+$

919 5-(17,7,18) (complement has $\lambda=48$)
$(A_4\times D_4)+$ (many isom. types)
TvT: 5-(16,6,3) $\cup$ 5-(16,7,12) \cite{TranvanTrung86}

959 5-(18,7,18) (complement has $\lambda=60$)
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

2794 5-(24,7,18) (complement has $\lambda=153$)
\cite{Kreheretal90}

3002 5-(24,8,18) (complement has $\lambda=951$)
$PSL(2,23)$ 2 isomorphism types

5411 5-(48,6,18) (complement has $\lambda=25$)
$PSL(2,47)$

3010 5-(24,8,19) (complement has $\lambda=950$)
$PSL(2,23)$ 1 isomorphism type

906 5-(16,7,20) (complement has $\lambda=35$)
$HoL(C_{16})$ Wassermann 152 solutions

310 5-(16,8,20) (complement has $\lambda=145$)
Alltop construction for design number 307
Alltop construction
Alltop construction

3014 5-(24,8,20) (complement has $\lambda=949$)
$PSL(2,23)$ 3 isomorphism types

3849 5-(25,7,20) (complement has $\lambda=170$)
TvT: 5-(24,6,2) $\cup$ 5-(24,7,18)

3861 5-(25,8,20) (complement has $\lambda=1120$)
TvT: 5-(24,7,3) $\cup$ 5-(24,8,17)

5419 5-(48,6,20) (complement has $\lambda=23$)
$PGL(2,23)\times C_2$

1510 5-(19,9,21) (complement has $\lambda=980$)
Brouwer 1977/1986

2797 5-(24,7,21) (complement has $\lambda=150$)
\cite{Kreheretal90}

3022 5-(24,8,21) (complement has $\lambda=948$)
$PSL(2,23)$ 6 isomorphism types

5423 5-(48,6,21) (complement has $\lambda=22$)
$PSL(2,47)$

291 5-(66,6,21) (complement has $\lambda=40$)
$P\Gamma L(2,32)\times C_2$

3026 5-(24,8,22) (complement has $\lambda=947$)
$PSL(2,23)$ 11 isomorphism types

4366 5-(28,7,22) (complement has $\lambda=231$)
$PSL(2,27)$ (>=1 isom. types)

3030 5-(24,8,23) (complement has $\lambda=946$)
$PSL(2,23)$ 18 isomorphism types

921 5-(17,7,24) (complement has $\lambda=42$)
Brouwer 1977/1986 $Hol(C_{17})$

963 5-(18,7,24) (complement has $\lambda=54$)
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
residual design of number 5524

2801 5-(24,7,24) (complement has $\lambda=147$)
\cite{Kreheretal90}

3034 5-(24,8,24) (complement has $\lambda=945$)
$PGL(2,23)$ 3 isomorphism types

4767 5-(29,7,24) (complement has $\lambda=252$)
$PGL(2,27)+$ (>=1 isom. types)

909 5-(16,7,25) (complement has $\lambda=30$)
$A_4\times A_4$

314 5-(16,8,25) (complement has $\lambda=140$)
Alltop construction for design number 311
Alltop construction
Alltop construction

3038 5-(24,8,25) (complement has $\lambda=944$)
$PSL(2,23)$ 49 isomorphism types

3042 5-(24,8,26) (complement has $\lambda=943$)
$PGL(2,23)$ 4 isomorphism types

2805 5-(24,7,27) (complement has $\lambda=144$)
\cite{Kreheretal90}

3046 5-(24,8,27) (complement has $\lambda=942$)
$PSL(2,23)$ 72 isomorphism types

1424 5-(19,7,28) (complement has $\lambda=63$)
$Hol(C_{19})$ (>=1 isom. types)
Brouwer 1977/1986
TvT: 5-(18,6,4) $\cup$ 5-(18,7,24) \cite{TranvanTrung86}
design of number 5524 with respect to smaller t

3050 5-(24,8,28) (complement has $\lambda=941$)
$PGL(2,23)$ 4 isomorphism types

4369 5-(28,7,28) (complement has $\lambda=225$)
$PSL(2,27)$ (>=1 isom. types)

3058 5-(24,8,29) (complement has $\lambda=940$)
$PSL(2,23)$

4373 5-(28,7,29) (complement has $\lambda=224$)
$PSL(2,27)$ (>=1 isom. types)

318 5-(16,8,30) (complement has $\lambda=135$)
Alltop construction for design number 315
Alltop construction

924 5-(17,7,30) (complement has $\lambda=36$)
TvT: 5-(16,6,5) $\cup$ 5-(16,7,25)

966 5-(18,7,30) (complement has $\lambda=48$)
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

1084 5-(18,8,30) (complement has $\lambda=256$)
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

1305 5-(18,9,30) (complement has $\lambda=685$)
\cite{Kramer75}
Alltop construction for design number 1307
\cite{Brouwer86} $Hol(C_17)+$ 1 isomorphism type

2812 5-(24,7,30) (complement has $\lambda=141$)
\cite{Kreheretal90}

3062 5-(24,8,30) (complement has $\lambda=939$)
$PGL(2,23)$ 4 isomorphism types

3850 5-(25,7,30) (complement has $\lambda=160$)
TvT: 5-(24,6,3) $\cup$ 5-(24,7,27)

1091 5-(18,8,32) (complement has $\lambda=254$)
\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types

7851 5-(22,7,32) (complement has $\lambda=104$)
residual design of number 7848
derived from number 7849

7849 6-(23,8,32) (complement has $\lambda=104$)
residual design of number 7847

3066 5-(24,8,32) (complement has $\lambda=937$)
$PGL(2,23)$ 8 isomorphism types

2816 5-(24,7,33) (complement has $\lambda=138$)
\cite{Kreheretal90}

3070 5-(24,8,34) (complement has $\lambda=935$)
$PGL(2,23)$ 9 isomorphism types

322 5-(16,8,35) (complement has $\lambda=130$)
Alltop construction for design number 319
Alltop construction

1062 5-(18,9,35) (complement has $\lambda=680$)
Alltop construction for design number 1059
\cite{Kramer75}
\cite{Brouwer86} $Hol(C_17)+$
\cite{Brouwer86} Alltop(res(5-(18,8,14))

1426 5-(19,7,35) (complement has $\lambda=56$)
Brouwer 1977/1986

1783 5-(20,8,35) (complement has $\lambda=420$)
\cite{Krameretal85} $PSL(2,19)$ 5 isomorphism types

3073 5-(24,8,35) (complement has $\lambda=934$)
$PGL(2,23)$ 1 isomorphism type

4377 5-(28,7,35) (complement has $\lambda=218$)
$PSL(2,27)$ (>=1 isom. types)

969 5-(18,7,36) (complement has $\lambda=42$)
\cite{Kramer75} $PGL(2,17)$ 4 isomorphism types
residual design of number 5525

1903 5-(22,7,36) (complement has $\lambda=100$)
$PSL(2,19)++$
$PGL(2,19)++$ 69 solutions

5749 5-(23,7,36) (complement has $\lambda=117$)
derived from number 5747
design of number 7848 with respect to smaller t

2820 5-(24,7,36) (complement has $\lambda=135$)
\cite{Kreheretal90}
derived from number 6251

3077 5-(24,8,36) (complement has $\lambda=933$)
$PGL(2,23)$ 13 isomorphism types

3607 5-(24,9,36) (complement has $\lambda=3840$)
\cite{Driessen78} $M_{24}$ 1 isomorphism type
$PSL(2,23)$ (4 solutions)

2488 5-(24,10,36) (complement has $\lambda=11592$)
$PSL(2,23)$ (1 isomorphism type) \cite{KitazumeMunemasa97} block-transitive

5747 6-(24,8,36) (complement has $\lambda=117$)
PGL(2,23) (9 isom. types) \cite{Bettenetal98b}
design of number 7847 with respect to smaller t

6251 6-(25,8,36) (complement has $\lambda=135$)
PGL(2,23)+ (242 isom. types) \cite{Bettenetal98b}

4381 5-(28,7,36) (complement has $\lambda=217$)
$PSL(2,27)$ (>=1 isom. types)
derived from number 7203

7203 6-(29,8,36) (complement has $\lambda=217$)
$P\Gamma L(2,27)+$ (8 isom. types) \cite{Bettenetal97b}

7663 5-(32,7,36) (complement has $\lambda=315$)
derived from number 7661

7661 6-(33,8,36) (complement has $\lambda=315$)
$P\Gamma L(2,32)$ (1179 isom. types) \cite{MagliverasLeavitt84}, \cite{Schmalz93}

3081 5-(24,8,37) (complement has $\lambda=932$)
$PGL(2,23)$ 1 isomorphism type

1098 5-(18,8,38) (complement has $\lambda=248$)
$C_2\times PGL(2,8)$ 129 solutions
$PSL(2,8)\times C_2$ (129 solutions)

3085 5-(24,8,38) (complement has $\lambda=931$)
$PGL(2,23)$ 24 isomorphism types

2823 5-(24,7,39) (complement has $\lambda=132$)
\cite{Kreheretal90}

3089 5-(24,8,39) (complement has $\lambda=930$)
$PGL(2,23)$ 4 isomorphism types

894 5-(15,8,40) (complement has $\lambda=80$)
supplementary design of number 893

326 5-(16,8,40) (complement has $\lambda=125$)
Alltop construction for design number 323
Alltop construction

1105 5-(18,8,40) (complement has $\lambda=246$)
$PGL(2,16)+$ 1 isomorphism type
\cite{MacWilliams78}

1083 5-(18,9,40) (complement has $\lambda=675$)
Alltop construction for design number 1080
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,16)) $Hol(C_17)+$

1907 5-(22,7,40) (complement has $\lambda=96$)
$PSL(2,19)++$
$PGL(2,19)++$ 92 solutions
$M_{11}\times C_2$ (2 isom. types)
residual design of number 7855
derived from number 7856

1919 5-(22,8,40) (complement has $\lambda=640$)
$PSL(2,19)++$ 10 solutions

7856 6-(23,8,40) (complement has $\lambda=96$)
residual design of number 7854
derived from number 7880

3097 5-(24,8,40) (complement has $\lambda=929$)
$PGL(2,23)$ 58 isomorphism types

7880 7-(24,9,40) (complement has $\lambda=96$)
PGL(2,23) (113 isom. types) \cite{Bettenetal98b}

3851 5-(25,7,40) (complement has $\lambda=150$)
TvT: 5-(24,6,4) $\cup$ 5-(24,7,36)

3863 5-(25,8,40) (complement has $\lambda=1100$)
TvT: 5-(24,7,6) $\cup$ 5-(24,8,34)

3101 5-(24,8,41) (complement has $\lambda=928$)
$PGL(2,23)$ 7 isomorphism types

1112 5-(18,8,42) (complement has $\lambda=244$)
$Id_2\times PGL(2,8)$ 738 solutions

1428 5-(19,7,42) (complement has $\lambda=49$)
Brouwer 1977/1986
design of number 5525 with respect to smaller t

1511 5-(19,10,42) (complement has $\lambda=1960$)
supplementary design of number 1510

2827 5-(24,7,42) (complement has $\lambda=129$)
\cite{Kreheretal90}

3105 5-(24,8,42) (complement has $\lambda=927$)
$PGL(2,23)$ 55 isomorphism types

3613 5-(24,9,42) (complement has $\lambda=3834$)
$PSL(2,23)$ (10 isomorphism types)

7046 5-(27,7,42) (complement has $\lambda=189$)
derived from number 7045

7208 5-(28,7,42) (complement has $\lambda=211$)
derived from number 7206

7045 6-(28,8,42) (complement has $\lambda=189$)
$P\Gamma L(2,27)$ (2 isom. types) \cite{Schmalz93}

7206 6-(29,8,42) (complement has $\lambda=211$)
$P\Gamma L(2,27)+$ (31 isom. types) \cite{Bettenetal97b}

5226 5-(33,7,42) (complement has $\lambda=336$)
\cite{Sebille98} $P\Gamma L(2,32)$

3109 5-(24,8,43) (complement has $\lambda=926$)
$PGL(2,23)$ 6 isomorphism types

4385 5-(28,7,43) (complement has $\lambda=210$)
$PSL(2,27)$ (>=1 isom. types)
derived from number 7216

7216 6-(29,8,43) (complement has $\lambda=210$)
$P\Gamma L(2,27)+$ (43 isom. types) \cite{Bettenetal97b}

1119 5-(18,8,44) (complement has $\lambda=242$)
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

3117 5-(24,8,44) (complement has $\lambda=925$)
$PGL(2,23)$ 48 isomorphism types

330 5-(16,8,45) (complement has $\lambda=120$)
Alltop construction for design number 327
$A_4\times D_4$ 1322 solutions
Alltop construction

1321 5-(18,9,45) (complement has $\lambda=670$)
\cite{Kramer75}
Alltop construction for design number 1323
\cite{Brouwer86} $Hol(C_17)+$

5758 5-(23,7,45) (complement has $\lambda=108$)
derived from number 5756
design of number 7855 with respect to smaller t

2831 5-(24,7,45) (complement has $\lambda=126$)
\cite{Kreheretal90}
derived from number 6256

3121 5-(24,8,45) (complement has $\lambda=924$)
$PGL(2,23)$ 4 isomorphism types

5756 6-(24,8,45) (complement has $\lambda=108$)
PGL(2,23) (49 isom. types) \cite{Bettenetal98b}
design of number 7854 with respect to smaller t
derived from number 7894

3895 5-(25,9,45) (complement has $\lambda=4800$)
TvT: 5-(24,8,9) $\cup$ 5-(24,9,36)

6256 6-(25,8,45) (complement has $\lambda=126$)
PGL(2,23)+ (10008 isom. types) \cite{Bettenetal98b}

7894 7-(25,9,45) (complement has $\lambda=108$)
(Tran van Trung construction): 7-(24,8,5) together with 7-(24,9,40) \cite{Bettenetal98b}

1125 5-(18,8,46) (complement has $\lambda=240$)
\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types $PGL(2,16)+$ 1 isomorphism type

3125 5-(24,8,46) (complement has $\lambda=923$)
$PGL(2,23)$ 79 isomorphism types

13 5-(28,7,46) (complement has $\lambda=207$)
TvT: 5-(27,6,4) $\cup$ 5-(27,7,42)

3129 5-(24,8,47) (complement has $\lambda=922$)
$PGL(2,23)$ 6 isomorphism types

1132 5-(18,8,48) (complement has $\lambda=238$)
$C_2\times PGL(2,8)$ 465 solutions
$PSL(2,8)\times C_2$ (465 solutions)
\cite{Kramer75} $PGL(2,17)$ 5 isomorphism types

7863 5-(22,7,48) (complement has $\lambda=88$)
residual design of number 7860
derived from number 7861

7861 6-(23,8,48) (complement has $\lambda=88$)
residual design of number 7859
derived from number 7884

2834 5-(24,7,48) (complement has $\lambda=123$)
\cite{Kreheretal90}

3133 5-(24,8,48) (complement has $\lambda=921$)
$PGL(2,23)$ 217 isomorphism types

3628 5-(24,9,48) (complement has $\lambda=3828$)
$PSL(2,23)$ (12 isomorphism types)

2722 5-(24,12,48) (complement has $\lambda=50340$)
\cite{AssmusMattson69c}
Alltop construction for design number 2724
\cite{Driessen}

7884 7-(24,9,48) (complement has $\lambda=88$)
PGL(2,23) (>= 2827 isom. types) \cite{Bettenetal98b}

3758 5-(25,10,48) (complement has $\lambda=15456$)
$PSL(2,23)+$ TvT construction 5-(24,9,12) $\cup$ 5-(24,10,36)

1655 5-(19,9,49) (complement has $\lambda=952$)
TvT: 5-(18,8,14) $\cup$ 5-(18,9,35) \cite{TranvanTrung86}

3137 5-(24,8,49) (complement has $\lambda=920$)
$PGL(2,23)$ 21 isomorphism types

7221 5-(28,7,49) (complement has $\lambda=204$)
derived from number 7219

7219 6-(29,8,49) (complement has $\lambda=204$)
$P\Gamma L(2,27)+$ (479 isom. types) \cite{Bettenetal97b}

334 5-(16,8,50) (complement has $\lambda=115$)
Alltop construction for design number 331
Alltop construction

1325 5-(18,9,50) (complement has $\lambda=665$)
\cite{Kramer75}
Alltop construction for design number 1327
\cite{Brouwer86} $Hol(C_17)+$

3141 5-(24,8,50) (complement has $\lambda=919$)
$PGL(2,23)$ 231 isomorphism types

3853 5-(25,7,50) (complement has $\lambda=140$)
TvT: 5-(24,6,5) $\cup$ 5-(24,7,45)

2838 5-(24,7,51) (complement has $\lambda=120$)
\cite{Kreheretal90}

3145 5-(24,8,51) (complement has $\lambda=918$)
$PGL(2,23)$ 27 isomorphism types

1139 5-(18,8,52) (complement has $\lambda=234$)
$PSL(2,8)\times Id_2$ (many solutions)

3148 5-(24,8,52) (complement has $\lambda=917$)
$PGL(2,23)$ 220 isomorphism types

3152 5-(24,8,53) (complement has $\lambda=916$)
$PGL(2,23)$

1145 5-(18,8,54) (complement has $\lambda=232$)
$Id_2\times PGL(2,8)$

5765 5-(23,7,54) (complement has $\lambda=99$)
derived from number 5763
design of number 7860 with respect to smaller t

2842 5-(24,7,54) (complement has $\lambda=117$)
\cite{Kreheretal90}
derived from number 6261
residual design of number 8000

3156 5-(24,8,54) (complement has $\lambda=915$)
$PGL(2,23)$

3639 5-(24,9,54) (complement has $\lambda=3822$)
$PGL(2,23)$ (1 isomorphism type)

5763 6-(24,8,54) (complement has $\lambda=99$)
PGL(2,23) (476 isom. types) \cite{Bettenetal98b}
design of number 7859 with respect to smaller t
derived from number 7895

6261 6-(25,8,54) (complement has $\lambda=117$)
PGL(2,23)+ \cite{Bettenetal98b}
residual design of number 7999
derived from number 8001

7895 7-(25,9,54) (complement has $\lambda=99$)
(Tran van Trung construction): 7-(24,8,6) together with 7-(24,9,48) \cite{Bettenetal98b}

8001 7-(26,9,54) (complement has $\lambda=117$)
$P\Gamma L(2,25)$ (3989 isom. types) \cite{Bettenetal98b}

338 5-(16,8,55) (complement has $\lambda=110$)
Alltop construction for design number 335
Tran van Trung construction with supplementary design for design number 893
Alltop construction

1329 5-(18,9,55) (complement has $\lambda=660$)
\cite{Kramer75}
Alltop construction for design number 1331
\cite{Brouwer86} $Hol(C_17)+$

3160 5-(24,8,55) (complement has $\lambda=914$)
$PGL(2,23)$

1152 5-(18,8,56) (complement has $\lambda=230$)
$C_2\times PGL(2,8)$ 1181 solutions

1435 5-(19,8,56) (complement has $\lambda=308$)
TvT: 5-(18,7,12) $\cup$ 5-(18,8,44) \cite{TranvanTrung86}

1670 5-(19,9,56) (complement has $\lambda=945$)
TvT: 5-(18,8,16) $\cup$ 5-(18,9,40) \cite{TranvanTrung86}

7870 5-(22,7,56) (complement has $\lambda=80$)
residual design of number 7867
derived from number 7868

7868 6-(23,8,56) (complement has $\lambda=80$)
residual design of number 7866

3164 5-(24,8,56) (complement has $\lambda=913$)
$PGL(2,23)$

4415 5-(28,8,56) (complement has $\lambda=1715$)
Bluskov

4795 5-(29,8,56) (complement has $\lambda=1968$)
$PGL(2,27)+$ (>=1 isom. types) #blocks = #5-subsets

2845 5-(24,7,57) (complement has $\lambda=114$)
\cite{Kreheretal90} $PGL(2,23))$ LS[3](5,7,24)

3168 5-(24,8,57) (complement has $\lambda=912$)
$PGL(2,23)$

7231 5-(28,7,57) (complement has $\lambda=196$)
derived from number 7229

7229 6-(29,8,57) (complement has $\lambda=196$)
$P\Gamma L(2,27)+$ (5177 isom. types) \cite{Bettenetal97b}

3172 5-(24,8,58) (complement has $\lambda=911$)
$PGL(2,23)$

3176 5-(24,8,59) (complement has $\lambda=910$)
$PGL(2,23)$

342 5-(16,8,60) (complement has $\lambda=105$)
Alltop construction for design number 339
$A_4\times A_4$
Alltop construction

933 5-(17,8,60) (complement has $\lambda=160$)
TvT: 5-(16,7,15) $\cup$ 5-(16,8,45) \cite{TranvanTrung86}

1166 5-(18,8,60) (complement has $\lambda=226$)
\cite{Kramer75} $PGL(2,17)$ 4 isomorphism types

1333 5-(18,9,60) (complement has $\lambda=655$)
\cite{Kramer75}
Alltop construction for design number 1335
\cite{Brouwer86} $Hol(C_17)+$

5555 5-(21,7,60) (selfcomplementary)
residual design of number 5553
residual design of complement of number 5553
derived from number 5559
derived from complement of number 5559

1911 5-(22,7,60) (complement has $\lambda=76$)
\cite{Kreher95} $PSL(2,19)++$
\cite{Kreher95} $PGL(2,19)++$

1923 5-(22,8,60) (complement has $\lambda=620$)
\cite{Kreher95} $PSL(2,19)++$
\cite{Kreher95}

5559 6-(22,8,60) (selfcomplementary)
PSL(2,19)++ (1148 isom types) \cite{Kreher93}, Halving of the complete design

2853 5-(24,7,60) (complement has $\lambda=111$)
\cite{Kreheretal90}

3180 5-(24,8,60) (complement has $\lambda=909$)
$PGL(2,23)$

3646 5-(24,9,60) (complement has $\lambda=3816$)
$PGL(2,23)$ (2 isomorphism types)

6296 5-(25,7,60) (complement has $\lambda=130$)
derived from number 6295
design of number 8000 with respect to smaller t

3865 5-(25,8,60) (complement has $\lambda=1080$)
TvT: 5-(24,7,9) $\cup$ 5-(24,8,51)

6295 6-(26,8,60) (complement has $\lambda=130$)
$P\Gamma L(2,25)$ (23 isomorphism types) \cite{Bettenetal97b}
\cite{Sebille98} $P\Gamma L(2,25)$
design of number 7999 with respect to smaller t
derived from number 8813

8813 7-(27,9,60) (complement has $\lambda=130$)
$P\Gamma L(2,25)+$, (Tran van Trung construction): 7-(26,8,6) together with 7-(26,9,54) \cite{Bettenetal98b}

3183 5-(24,8,61) (complement has $\lambda=908$)
$PGL(2,23)$

1173 5-(18,8,62) (complement has $\lambda=224$)
$C_2\times PGL(2,8)$ 1419 solutions
$PSL(2,8)\times C_2$ (1419 solutions)
\cite{Kramer75} $PGL(2,17)$ 5 isomorphism types

3187 5-(24,8,62) (complement has $\lambda=907$)
$PGL(2,23)$

1513 5-(20,10,63) (complement has $\lambda=2940$)
Tran van Trung construction with supplementary design for design number 1510
Alltop construction for design number 1512
\cite{Krameretal85}

5773 5-(23,7,63) (complement has $\lambda=90$)
derived from number 5771
design of number 7867 with respect to smaller t

2857 5-(24,7,63) (complement has $\lambda=108$)
\cite{Driessen78}
derived from number 6265

3191 5-(24,8,63) (complement has $\lambda=906$)
$PGL(2,23)$

5771 6-(24,8,63) (complement has $\lambda=90$)
PGL(2,23) (1284 isom. types) \cite{Bettenetal98b}
design of number 7866 with respect to smaller t

6265 6-(25,8,63) (complement has $\lambda=108$)
PGL(2,23)+ \cite{Bettenetal98b}
$AGL(2,5)^2$
derived from number 8003

3911 5-(26,10,63) (complement has $\lambda=20286$)
TvT: 5-(25,9,15) $\cup$ 5-(25,10,48)

8003 7-(26,9,63) (complement has $\lambda=108$)
$P\Gamma L(2,25)$ (37932 isom. types) \cite{Bettenetal98b}

46 5-(27,7,63) (complement has $\lambda=168$)
residual design of number 44
derived from number 7050

7241 5-(28,7,63) (complement has $\lambda=190$)
derived from number 7239

7050 6-(28,8,63) (complement has $\lambda=168$)
$P\Gamma L(2,27)$ (367 isom. types) \cite{Schmalz93}

7239 6-(29,8,63) (complement has $\lambda=190$)
$P\Gamma L(2,27)+$ (17195 isom. types) \cite{Bettenetal97b}

1180 5-(18,8,64) (complement has $\lambda=222$)
\cite{Kramer75} $PGL(2,17)$ 8 isomorphism types

7877 5-(22,7,64) (complement has $\lambda=72$)
residual design of number 7874
derived from number 7875

7875 6-(23,8,64) (complement has $\lambda=72$)
residual design of number 7873
derived from number 7886

3195 5-(24,8,64) (complement has $\lambda=905$)
$PGL(2,23)$

7886 7-(24,9,64) (complement has $\lambda=72$)
PGL(2,23) (>= 15335 isom. types) \cite{Bettenetal98b}

7250 5-(28,7,64) (complement has $\lambda=189$)
derived from number 7249

4802 5-(29,8,64) (complement has $\lambda=1960$)
$PGL(2,27)+$ (>=1 isom. types)

7249 6-(29,8,64) (complement has $\lambda=189$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

346 5-(16,8,65) (complement has $\lambda=100$)
Alltop construction for design number 343
$A_4\times A_4$
Alltop construction

1337 5-(18,9,65) (complement has $\lambda=650$)
\cite{Kramer75}
Alltop construction for design number 1339
\cite{Brouwer86} $Hol(C_17)+$

9556 5-(31,7,65) (complement has $\lambda=260$)
derived from number 9551

9551 6-(32,8,65) (complement has $\lambda=260$)
derived from number 9549

9549 7-(33,9,65) (complement has $\lambda=260$)
$P\Gamma L(2,32)$ (many isomorphism types)

1187 5-(18,8,66) (complement has $\lambda=220$)
$PSL(2,8)\times Id_2$ (many solutions)
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

2860 5-(24,7,66) (complement has $\lambda=105$)
\cite{Kreheretal90}

3649 5-(24,9,66) (complement has $\lambda=3810$)
$PGL(2,23)$ (2 isomorphism types)

1915 5-(22,7,68) (selfcomplementary)
\cite{Kreher95}
design of number 5553 with respect to smaller t
complementary design of number 5553 with respect to smaller t
derived from number 5658
derived from complement of number 5658

5658 6-(23,8,68) (selfcomplementary)
\cite{Kreher93} Halving of the complete design

2864 5-(24,7,69) (complement has $\lambda=102$)
\cite{Kreheretal90}

29 5-(28,7,69) (complement has $\lambda=184$)
derived from number 28
design of number 44 with respect to smaller t

28 6-(29,8,69) (complement has $\lambda=184$)
TvT: 6-(28,7,6) $\cup$ 6-(28,8,63)

350 5-(16,8,70) (complement has $\lambda=95$)
Alltop construction for design number 347
Alltop construction

1193 5-(18,8,70) (complement has $\lambda=216$)
$C_2\times PGL(2,8)$ 12426 solutions
$PSL(2,8)\times C_2$ (12426 solutions)

1341 5-(18,9,70) (complement has $\lambda=645$)
\cite{Kramer75}
Alltop construction for design number 1343

1787 5-(20,8,70) (complement has $\lambda=385$)
\cite{Krameretal85} $PGL(2,19)$ 3 isomorphism types

3199 5-(24,8,70) (complement has $\lambda=899$)
$PSL(2,23)$

6299 5-(25,7,70) (complement has $\lambda=120$)
derived from number 6297

3973 5-(26,8,70) (complement has $\lambda=1260$)
$PSL(2,25)$

6297 6-(26,8,70) (complement has $\lambda=120$)
$P\Gamma L(2,25)$ (87 isomorphism types) \cite{Bettenetal97b}

7256 5-(28,7,70) (complement has $\lambda=183$)
derived from number 7254

7254 6-(29,8,70) (complement has $\lambda=183$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

5265 5-(34,7,70) (complement has $\lambda=336$)
\cite{Sebille98} $P\Gamma L(2,16)\times C_2$

5780 5-(23,7,72) (complement has $\lambda=81$)
derived from number 5778
design of number 7874 with respect to smaller t

2868 5-(24,7,72) (complement has $\lambda=99$)
\cite{Kreheretal90}
derived from number 6270

3203 5-(24,8,72) (complement has $\lambda=897$)
$PGL(2,23)$

3662 5-(24,9,72) (complement has $\lambda=3804$)
$PGL(2,23)$ (7 isomorphism types)

2611 5-(24,10,72) (complement has $\lambda=11556$)
$PGL(2,23)$ (1 isomorphism type) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (1 isomorphism type) \cite{KitazumeMunemasa97}

5778 6-(24,8,72) (complement has $\lambda=81$)
PGL(2,23) (3069 isom. types) \cite{Bettenetal98b}
design of number 7873 with respect to smaller t
derived from number 7898

6270 6-(25,8,72) (complement has $\lambda=99$)
PGL(2,23)+ \cite{Bettenetal98b}

7898 7-(25,9,72) (complement has $\lambda=81$)
(Tran van Trung construction): 7-(24,8,8) together with 7-(24,9,64) \cite{Bettenetal98b}

82 5-(64,7,72) (complement has $\lambda=1639$)
$ASL(3,4)$
$A\Sigma L(3,4)$ many solutions

354 5-(16,8,75) (complement has $\lambda=90$)
Alltop construction for design number 351
Alltop construction

1090 5-(18,9,75) (complement has $\lambda=640$)
Alltop construction for design number 1087
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,30))

2871 5-(24,7,75) (complement has $\lambda=96$)
\cite{Kreheretal90}

7656 5-(31,7,75) (complement has $\lambda=250$)
residual design of number 7653

5280 5-(35,7,75) (complement has $\lambda=360$)
TvT: 5-(34,6,5) $\cup$ 5-(34,7,70)

1200 5-(18,8,76) (complement has $\lambda=210$)
$PSL(2,8)\times Id_2$ (many solutions)
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types

3207 5-(24,8,76) (complement has $\lambda=893$)
$PGL(2,23)$

1207 5-(18,8,78) (complement has $\lambda=208$)
\cite{Kramer75}
\cite{Kramer75} $PGL(2,17)$ 8 isomorphism types TvT: 5-(17,7,18) $\cup$ 5-(17,8,60) \cite{TranvanTrung86}

2875 5-(24,7,78) (complement has $\lambda=93$)
\cite{Kreheretal90}

3680 5-(24,9,78) (complement has $\lambda=3798$)
$PGL(2,23)$ (6 isomorphism types)

2924 5-(24,16,78) (complement has $\lambda=75504$)
\cite{Driessen}

7266 5-(28,7,78) (complement has $\lambda=175$)
derived from number 7264

7264 6-(29,8,78) (complement has $\lambda=175$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

358 5-(16,8,80) (complement has $\lambda=85$)
Alltop construction for design number 355
Alltop construction

940 5-(17,8,80) (complement has $\lambda=140$)
\cite{Kramer75} $PGL(2,16)$

1209 5-(18,8,80) (complement has $\lambda=206$)
$C_2\times PGL(2,8)$
\cite{Kramer75} $PGL(2,17)$ 9 isomorphism types

1097 5-(18,9,80) (complement has $\lambda=635$)
Alltop construction for design number 1094
\cite{Brouwer86} $Hol(C_17)+$
\cite{Brouwer86} Alltop(res(5-(18,8,32))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

1927 5-(22,8,80) (complement has $\lambda=600$)
\cite{Kreher95} $PSL(2,19)++$
\cite{Kreher95}

3211 5-(24,8,80) (complement has $\lambda=889$)
$PGL(2,23)$

3855 5-(25,7,80) (complement has $\lambda=110$)
TvT: 5-(24,6,8) $\cup$ 5-(24,7,72)

9575 5-(31,7,80) (complement has $\lambda=245$)
derived from number 9570

9570 6-(32,8,80) (complement has $\lambda=245$)
derived from number 9568

9568 7-(33,9,80) (complement has $\lambda=245$)
$P\Gamma L(2,32)$ (many isomorphism types)

2879 5-(24,7,81) (complement has $\lambda=90$)
\cite{Kreheretal90}
derived from number 6273

6273 6-(25,8,81) (complement has $\lambda=90$)
PGL(2,23)+ \cite{Bettenetal98b}
derived from number 8007

8007 7-(26,9,81) (complement has $\lambda=90$)
$P\Gamma L(2,25)$ (many isom. types) \cite{Bettenetal98b}

7654 5-(32,7,81) (complement has $\lambda=270$)
design of number 7653 with respect to smaller t

1216 5-(18,8,82) (complement has $\lambda=204$)
\cite{Kramer75}
\cite{Kramer75} $PGL(2,17)$ 4 isomorphism types

1223 5-(18,8,84) (complement has $\lambda=202$)
$Id_2\times PGL(2,8)$

1437 5-(19,8,84) (complement has $\lambda=280$)
TvT: 5-(18,7,18) $\cup$ 5-(18,8,66) \cite{TranvanTrung86}

2881 5-(24,7,84) (complement has $\lambda=87$)
\cite{Kreheretal90}

3691 5-(24,9,84) (complement has $\lambda=3792$)
$PGL(2,23)$ (11 isomorphism types)

7054 5-(27,7,84) (complement has $\lambda=147$)
derived from number 7053

7276 5-(28,7,84) (complement has $\lambda=169$)
derived from number 7274

7053 6-(28,8,84) (complement has $\lambda=147$)
$P\Gamma L(2,27)$ (21743 isom types) \cite{Schmalz93}

4769 5-(29,7,84) (complement has $\lambda=192$)
$PGL(2,27)+$ (>=1 isom. types)

7274 6-(29,8,84) (complement has $\lambda=169$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

1345 5-(18,9,85) (complement has $\lambda=630$)
\cite{Kramer75}
Alltop construction for design number 1347

7286 5-(28,7,85) (complement has $\lambda=168$)
derived from number 7284

7284 6-(29,8,85) (complement has $\lambda=168$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

9595 5-(31,7,85) (complement has $\lambda=240$)
derived from number 9590

9590 6-(32,8,85) (complement has $\lambda=240$)
derived from number 9588

9588 7-(33,9,85) (complement has $\lambda=240$)
$P\Gamma L(2,32)$ (many isomorphism types)

3215 5-(24,8,88) (complement has $\lambda=881$)
$PGL(2,23)$

1230 5-(18,8,90) (complement has $\lambda=196$)
$Id_2\times PGL(2,8)$
$PSL(2,8)\times Id_2$ (many solutions)

1349 5-(18,9,90) (complement has $\lambda=625$)
\cite{Kramer75}
Alltop construction for design number 1351
\cite{Brouwer86} $Hol(C_17)+$

3705 5-(24,9,90) (complement has $\lambda=3786$)
$PGL(2,23)$ (17 isomorphism types)

3857 5-(25,7,90) (complement has $\lambda=100$)
TvT: 5-(24,6,9) $\cup$ 5-(24,7,81)

3897 5-(25,9,90) (complement has $\lambda=4755$)
TvT: 5-(24,8,18) $\cup$ 5-(24,9,72)

4872 5-(30,7,90) (complement has $\lambda=210$)
$PSL(2,29)$ many solutions

7292 5-(28,7,91) (complement has $\lambda=162$)
derived from number 7290

7290 6-(29,8,91) (complement has $\lambda=162$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

1237 5-(18,8,92) (complement has $\lambda=194$)
\cite{Kramer75} $PGL(2,17)$ 8 isomorphism types

3219 5-(24,8,92) (complement has $\lambda=877$)
$PGL(2,23)$

4397 5-(28,7,93) (complement has $\lambda=160$)
$S_8^{[2]}$ (1 isom. type)
derived from number 10657

10657 6-(29,8,93) (complement has $\lambda=160$)
derived from number 10655

10655 7-(30,9,93) (complement has $\lambda=160$)
derived from number 10654

10654 8-(31,10,93) (complement has $\lambda=160$)
$PSL(3,5)$ (138 isom. types) \cite{Bettenetal98}

1244 5-(18,8,94) (complement has $\lambda=192$)
\cite{Kramer75} $PGL(2,17)$ 9 isomorphism types
$C_2\times PGL(2,8)$
$PSL(2,8)\times C_2$ (many solutions)

1104 5-(18,9,95) (complement has $\lambda=620$)
Alltop construction for design number 1101
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

1251 5-(18,8,96) (complement has $\lambda=190$)
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types

2393 5-(23,8,96) (complement has $\lambda=720$)
TvT: 5-(22,7,16) $\cup$ 5-(22,8,80)

3223 5-(24,8,96) (complement has $\lambda=873$)
$PGL(2,23)$

3712 5-(24,9,96) (complement has $\lambda=3780$)
$PGL(2,23)$ (43 isomorphism types)

1258 5-(18,8,98) (complement has $\lambda=188$)
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types

1656 5-(19,10,98) (complement has $\lambda=1904$)
supplementary design of number 1655

7302 5-(28,7,99) (complement has $\lambda=154$)
derived from number 7300

7300 6-(29,8,99) (complement has $\lambda=154$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

926 5-(17,8,100) (complement has $\lambda=120$)
TvT: 5-(16,7,25) $\cup$ 5-(16,8,75)

1111 5-(18,9,100) (complement has $\lambda=615$)
Alltop construction for design number 1108
\cite{Kramer75}
\cite{Brouwer86} $Hol(C_17)+$
\cite{Brouwer86} Alltop(res(5-(18,8,40))
\cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type

1930 5-(22,8,100) (complement has $\lambda=580$)
\cite{Kreher95} $PSL(2,19)++$
\cite{Kreher95}

2928 5-(24,8,100) (complement has $\lambda=869$)
$PGL(2,23)$

10650 5-(28,7,100) (complement has $\lambda=153$)
derived from number 10647

10647 6-(29,8,100) (complement has $\lambda=153$)
derived from number 10645

4876 5-(30,8,100) (complement has $\lambda=2200$)
\cite{Kreher95}

10645 7-(30,9,100) (complement has $\lambda=153$)
derived from number 10644

9439 5-(31,7,100) (complement has $\lambda=225$)
derived from number 9434

10644 8-(31,10,100) (complement has $\lambda=153$)
$PSL(3,5)$ (1658 isom. types) \cite{Bettenetal98}

9434 6-(32,8,100) (complement has $\lambda=225$)
derived from number 9432

9432 7-(33,9,100) (complement has $\lambda=225$)
$P\Gamma L(2,32)$ (many isomorphism types)

3231 5-(24,9,102) (complement has $\lambda=3774$)
$PGL(2,23)$ (38 isomorphism types)

977 5-(18,8,104) (complement has $\lambda=182$)
$C_2\times PGL(2,8)$
$PSL(2,8)\times C_2$ (many solutions)
\cite{Kramer75}
TvT: 5-(17,7,24) $\cup$ 5-(17,8,80) \cite{TranvanTrung86}

2932 5-(24,8,104) (complement has $\lambda=865$)
$PGL(2,23)$

1118 5-(18,9,105) (complement has $\lambda=610$)
Alltop construction for design number 1115
$PSL(2,8)\times C_2$ 48 solutions
\cite{Kramer75}

1439 5-(19,9,105) (complement has $\lambda=896$)
TvT: 5-(18,8,30) $\cup$ 5-(18,9,75) \cite{TranvanTrung86}

1773 5-(20,8,105) (complement has $\lambda=350$)
TvT: 5-(19,7,21) $\cup$ 5-(19,8,84) \cite{TranvanTrung86}
\cite{Krameretal85} $PGL(2,19)$ 64 isomorphism types

1790 5-(20,9,105) (complement has $\lambda=1260$)
\cite{Krameretal85} $PGL(2,19)$ 1 isomorphism type

3867 5-(25,9,105) (complement has $\lambda=4740$)
TvT: 5-(24,8,21) $\cup$ 5-(24,9,84)

7040 5-(27,7,105) (complement has $\lambda=126$)
derived from number 7039

7165 5-(28,7,105) (complement has $\lambda=148$)
derived from number 7163

7309 5-(28,8,105) (complement has $\lambda=1666$)
derived from number 7307

7039 6-(28,8,105) (complement has $\lambda=126$)
$P\Gamma L(2,27)$ (38277 isom. types) \cite{Schmalz93}

7163 6-(29,8,105) (complement has $\lambda=148$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}
derived from number 9278

7307 6-(29,9,105) (complement has $\lambda=1666$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

9278 7-(30,9,105) (complement has $\lambda=148$)
$P\Gamma L(2,27)++$ (>= 1) \cite{Bettenetal97b}

9456 5-(31,7,105) (complement has $\lambda=220$)
derived from number 9454

9454 6-(32,8,105) (complement has $\lambda=220$)
derived from number 9452

9452 7-(33,9,105) (complement has $\lambda=220$)
$P\Gamma L(2,32)$ (many isomorphism types)

7174 5-(28,7,106) (complement has $\lambda=147$)
derived from number 7172

7172 6-(29,8,106) (complement has $\lambda=147$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

979 5-(18,8,108) (complement has $\lambda=178$)
\cite{Kramer75} $PGL(2,17)$ 12 isomorphism types

3238 5-(24,9,108) (complement has $\lambda=3768$)
$PGL(2,23)$ (152 isomorphism types)

2401 5-(24,10,108) (complement has $\lambda=11520$)
$PSL(2,23)$ (7 isomorphism types) \cite{KitazumeMunemasa97}

4764 5-(29,7,108) (complement has $\lambda=168$)
$PGL(2,27)+$ (>=1 isom. types)
derived from number 7551

7551 6-(30,8,108) (complement has $\lambda=168$)
$PGGL(2,27)++$ (many isom. types)

986 5-(18,8,110) (complement has $\lambda=176$)
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types $PGL(2,16)+$ 32 isomorphism types

1124 5-(18,9,110) (complement has $\lambda=605$)
Alltop construction for design number 1121
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,44))

992 5-(18,8,112) (complement has $\lambda=174$)
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types

5534 5-(19,8,112) (complement has $\lambda=252$)
derived from number 5533

1446 5-(19,9,112) (complement has $\lambda=889$)
TvT: 5-(18,8,32) $\cup$ 5-(18,9,80) \cite{TranvanTrung86}

1671 5-(19,10,112) (complement has $\lambda=1890$)
supplementary design of number 1670

5533 6-(20,9,112) (complement has $\lambda=252$)
$PSL(2,19)$ (2 isom. types) \cite{Krameretal85}
$PSL(2,9)\times C_2$ many solutions
$C_2\times PGL(2,9)$ 196 solutions

2936 5-(24,8,112) (complement has $\lambda=857$)
$PGL(2,23)$

7184 5-(28,7,112) (complement has $\lambda=141$)
derived from number 7182

7182 6-(29,8,112) (complement has $\lambda=141$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}
derived from number 9279

9279 7-(30,9,112) (complement has $\lambda=141$)
$P\Gamma L(2,27)++$ (many) \cite{Bettenetal97b}

999 5-(18,8,114) (complement has $\lambda=172$)
\cite{Kramer75} $PGL(2,17)$ 9 isomorphism types

3264 5-(24,9,114) (complement has $\lambda=3762$)
$PGL(2,23)$ (205 isomorphism types)

1131 5-(18,9,115) (complement has $\lambda=600$)
Alltop construction for design number 1128
\cite{Brouwer86} Alltop(res(5-(18,8,46))
\cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type

7813 5-(18,8,116) (complement has $\lambda=170$)
derived from number 7811

7811 6-(19,9,116) (complement has $\lambda=170$)
derived from number 7810

7810 7-(20,10,116) (complement has $\lambda=170$)
PSL(2,19) (3 isom. types) \cite{Bettenetal97b}
Alltop construction for design number 7811

2940 5-(24,8,116) (complement has $\lambda=853$)
$PGL(2,23)$

1006 5-(18,8,118) (complement has $\lambda=168$)
$C_2\times PGL(2,8)$
$PSL(2,8)\times C_2$ (many solutions)

1138 5-(18,9,120) (complement has $\lambda=595$)
Alltop construction for design number 1135
\cite{Brouwer86} Alltop(res(5-(18,8,48))
\cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

1934 5-(22,8,120) (complement has $\lambda=560$)
$PSL(2,19)++$
$S_7^{[2]}+$ (3 isom. types)

2944 5-(24,8,120) (complement has $\lambda=849$)
$PGL(2,23)$

3296 5-(24,9,120) (complement has $\lambda=3756$)
$PGL(2,23)$ (326 isomorphism types)

3869 5-(25,9,120) (complement has $\lambda=4725$)
TvT: 5-(24,8,24) $\cup$ 5-(24,9,96)

7193 5-(28,7,120) (complement has $\lambda=133$)
derived from number 7191

4772 5-(29,8,120) (complement has $\lambda=1904$)
TvT: 5-(28,7,15) $\cup$ 5-(28,8,105)

7191 6-(29,8,120) (complement has $\lambda=133$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

9466 5-(31,7,120) (complement has $\lambda=205$)
derived from number 9461

9461 6-(32,8,120) (complement has $\lambda=205$)
derived from number 9459

9459 7-(33,9,120) (complement has $\lambda=205$)
$P\Gamma L(2,32)$ (many isomorphism types)

5460 5-(64,7,120) (complement has $\lambda=1591$)
$A\Sigma L(3,4)$ many solutions

1013 5-(18,8,122) (complement has $\lambda=164$)
$Id_2\times PGL(2,8)$

1020 5-(18,8,124) (complement has $\lambda=162$)
\cite{Kramer75} $PGL(2,17)$ 15 isomorphism types
derived from number 7818

7818 6-(19,9,124) (complement has $\lambda=162$)
derived from number 7817

7817 7-(20,10,124) (complement has $\lambda=162$)
PSL(2,19) (1 isom. type) \cite{Bettenetal97b}
Alltop construction for design number 7818

1265 5-(18,9,125) (complement has $\lambda=590$)
\cite{Kramer75}
Alltop construction for design number 1267

9423 5-(31,7,125) (complement has $\lambda=200$)
residual design of number 9418
derived from number 9419

9419 6-(32,8,125) (complement has $\lambda=200$)
residual design of number 9416
derived from number 9479

9479 7-(33,9,125) (complement has $\lambda=200$)
$P\Gamma L(2,32)$ (many isomorphism types)

1027 5-(18,8,126) (complement has $\lambda=160$)
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types
$C_2\times PGL(2,8)$
$PSL(2,8)\times C_2$ (many solutions)
derived from number 5527

5527 6-(19,9,126) (complement has $\lambda=160$)
$(PSL(2,8)\times C_2)+$ (24 solutions)
derived from number 5530

1693 5-(20,10,126) (complement has $\lambda=2877$)
\cite{Krameretal85} $PSL(2,19)$ 2 isomorphism types
Alltop construction for design number 1695

5530 7-(20,10,126) (complement has $\lambda=160$)
Alltop construction for design number 5527
$(PGL(2,8)\times C_2)++$(24 solutions, 4 isomorphism types), Alltop construction from 6-(19,9,126)

3302 5-(24,9,126) (complement has $\lambda=3750$)
$PGL(2,23)$ (>1 isomorphism types)

2405 5-(24,10,126) (complement has $\lambda=11502$)
$PSL(2,23)$ (2 isomorphism types) \cite{KitazumeMunemasa97}

4358 5-(28,7,126) (complement has $\lambda=127$)
$PSL(2,27)$ (many isom. types)
derived from number 7197

7316 5-(28,8,126) (complement has $\lambda=1645$)
derived from number 7314

7197 6-(29,8,126) (complement has $\lambda=127$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

7314 6-(29,9,126) (complement has $\lambda=1645$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

5218 5-(33,7,126) (complement has $\lambda=252$)
\cite{Sebille98} $P\Gamma L(2,32)$

1034 5-(18,8,128) (complement has $\lambda=158$)
\cite{Kramer75} $PGL(2,17)$ 5 isomorphism types

2948 5-(24,8,128) (complement has $\lambda=841$)
\cite{Driessen78} $M_{24}$ 1 isomorphism type

2952 5-(24,8,129) (complement has $\lambda=840$)
\cite{Driessen78} $M_{24}$ 1 isomorphism type

1041 5-(18,8,130) (complement has $\lambda=156$)
\cite{Kramer75} $PGL(2,17)$ 11 isomorphism types

1144 5-(18,9,130) (complement has $\lambda=585$)
Alltop construction for design number 1141
\cite{Kramer75}
\cite{Brouwer86} $Hol(C_17)+$

1043 5-(18,8,132) (complement has $\lambda=154$)
$Id_2\times PGL(2,8)$
$PSL(2,8)\times Id_2$ (many solutions)

2956 5-(24,8,132) (complement has $\lambda=837$)
$PGL(2,23)$

3325 5-(24,9,132) (complement has $\lambda=3744$)
$PGL(2,23)$ (>1 isomorphism types)
$PSL(2,23)$

1453 5-(19,9,133) (complement has $\lambda=868$)
TvT: 5-(18,8,38) $\cup$ 5-(18,9,95)

7825 5-(18,8,134) (complement has $\lambda=152$)
derived from number 7823

7823 6-(19,9,134) (complement has $\lambda=152$)
derived from number 7822

7822 7-(20,10,134) (complement has $\lambda=152$)
PSL(2,19) (10 isom. types) \cite{Bettenetal97b}
Alltop construction for design number 7823

934 5-(17,9,135) (complement has $\lambda=360$)
supplementary design of number 933

1151 5-(18,9,135) (complement has $\lambda=580$)
Alltop construction for design number 1148
\cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type
\cite{Kramer75} $PSL(2,17)$ 2 isomorphism types

3871 5-(25,9,135) (complement has $\lambda=4710$)
TvT: 5-(24,8,27) $\cup$ 5-(24,9,108)

9421 5-(32,7,135) (complement has $\lambda=216$)
derived from number 9417
design of number 9418 with respect to smaller t

9417 6-(33,8,135) (complement has $\lambda=216$)
design of number 9416 with respect to smaller t
derived from number 9609

9609 7-(34,9,135) (complement has $\lambda=216$)
$P\Gamma L(2,32)+$ (many isomorphism types)

1049 5-(18,8,136) (complement has $\lambda=150$)
$C_2\times PGL(2,8)$

2960 5-(24,8,136) (complement has $\lambda=833$)
$PGL(2,23)$

3352 5-(24,9,138) (complement has $\lambda=3738$)
$PGL(2,23)$ (>1 isomorphism types)
$PSL(2,23)$

7544 5-(29,7,138) (selfcomplementary)
residual design of number 7541
residual design of complement of number 7541

1063 5-(18,8,140) (complement has $\lambda=146$)
\cite{Kramer75} $PGL(2,17)$ 14 isomorphism types

1158 5-(18,9,140) (complement has $\lambda=575$)
Alltop construction for design number 1155
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75} $PSL(2,17)$ 1 isomorphism type

1431 5-(19,8,140) (complement has $\lambda=224$)
TvT: 5-(18,7,30) $\cup$ 5-(18,8,110) \cite{TranvanTrung86}

1460 5-(19,9,140) (complement has $\lambda=861$)
Brouwer 1977/1986

1776 5-(20,8,140) (complement has $\lambda=315$)
\cite{Krameretal85} $PGL(2,19)$ 365 isomorphism types
TvT: 5-(19,7,28) $\cup$ 5-(19,8,112)

1884 5-(21,9,140) (complement has $\lambda=1680$)
TvT: 5-(20,8,35) $\cup$ 5-(20,9,105) \cite{TranvanTrung86}

1938 5-(22,8,140) (complement has $\lambda=540$)
$PSL(2,19)++$

2963 5-(24,8,140) (complement has $\lambda=829$)
$PGL(2,23)$

9496 5-(31,7,140) (complement has $\lambda=185$)
derived from number 9491

9491 6-(32,8,140) (complement has $\lambda=185$)
derived from number 9489

5230 5-(33,8,140) (complement has $\lambda=3136$)
\cite{Sebille98} $P\Gamma L(2,32)$

9489 7-(33,9,140) (complement has $\lambda=185$)
$P\Gamma L(2,32)$ (many isomorphism types)

1070 5-(18,8,142) (complement has $\lambda=144$)
\cite{Kramer75} $PGL(2,17)$ 5 isomorphism types

2967 5-(24,8,144) (complement has $\lambda=825$)
$PGL(2,23)$

3375 5-(24,9,144) (complement has $\lambda=3732$)
$PGL(2,23)$ (>1 isomorphism types)

2409 5-(24,10,144) (complement has $\lambda=11484$)
$PGL(2,23)$ (1 isomorphism type) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (20 isomorphism types) \cite{KitazumeMunemasa97}

3726 5-(25,10,144) (complement has $\lambda=15360$)
TvT: 5-(24,9,36) $\cup$ 5-(24,10,108)

1269 5-(18,9,145) (complement has $\lambda=570$)
\cite{Kramer75}
Alltop construction for design number 1271

9516 5-(31,7,145) (complement has $\lambda=180$)
derived from number 9511

9511 6-(32,8,145) (complement has $\lambda=180$)
derived from number 9509

9509 7-(33,9,145) (complement has $\lambda=180$)
$P\Gamma L(2,32)$ (many isomorphism types)
$P\Gamma L(2,32)$ (many isomorphism types)

1467 5-(19,9,147) (complement has $\lambda=854$)
TvT: 5-(18,8,42) $\cup$ 5-(18,9,105)

1658 5-(20,10,147) (complement has $\lambda=2856$)
Tran van Trung construction with supplementary design for design number 1655
Alltop construction for design number 1657
\cite{Krameretal85} $PSL(2,19)$ 36 isomorphism types

1172 5-(18,9,150) (complement has $\lambda=565$)
Alltop construction for design number 1169
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,60))

3393 5-(24,9,150) (complement has $\lambda=3726$)
$PGL(2,23)$ (>1 isomorphism types)

3877 5-(25,9,150) (complement has $\lambda=4695$)
TvT: 5-(24,8,30) $\cup$ 5-(24,9,120)

7542 5-(30,7,150) (selfcomplementary)
design of number 7541 with respect to smaller t
complementary design of number 7541 with respect to smaller t

2971 5-(24,8,152) (complement has $\lambda=817$)
$PGL(2,23)$

1474 5-(19,9,154) (complement has $\lambda=847$)
TvT: 5-(18,8,44) $\cup$ 5-(18,9,110) \cite{TranvanTrung86}

7326 5-(28,8,154) (complement has $\lambda=1617$)
derived from number 7324

7324 6-(29,9,154) (complement has $\lambda=1617$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

1179 5-(18,9,155) (complement has $\lambda=560$)
Alltop construction for design number 1176
\cite{Brouwer86} Alltop(res(5-(18,8,62))
\cite{Kramer75} $PSL(2,17)$ 1 isomorphism type

2975 5-(24,8,156) (complement has $\lambda=813$)
$PGL(2,23)$

3420 5-(24,9,156) (complement has $\lambda=3720$)
$PGL(2,23)$ (>1 isomorphism types)

1186 5-(18,9,160) (complement has $\lambda=555$)
Alltop construction for design number 1183
\cite{Brouwer86} Alltop(res(5-(18,8,64))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
\cite{Kramer75} $PSL(2,17)$ 1 isomorphism type

1942 5-(22,8,160) (complement has $\lambda=520$)
$PSL(2,19)++$
residual design of number 7849

2983 5-(24,8,160) (complement has $\lambda=809$)
$PGL(2,23)$

3859 5-(25,8,160) (complement has $\lambda=980$)
TvT: 5-(24,7,24) $\cup$ 5-(24,8,136)

9536 5-(31,7,160) (complement has $\lambda=165$)
derived from number 9531

9531 6-(32,8,160) (complement has $\lambda=165$)
derived from number 9529

9529 7-(33,9,160) (complement has $\lambda=165$)
$P\Gamma L(2,32)$ (many isomorphism types)

1478 5-(19,9,161) (complement has $\lambda=840$)
TvT: 5-(18,8,46) $\cup$ 5-(18,9,115) \cite{TranvanTrung86}

2413 5-(24,10,162) (complement has $\lambda=11466$)
$PSL(2,23)$ (28 isomorphism types) \cite{KitazumeMunemasa97}

2987 5-(24,8,164) (complement has $\lambda=805$)
$PGL(2,23)$

1192 5-(18,9,165) (complement has $\lambda=550$)
Alltop construction for design number 1189
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,66))

5338 5-(36,7,165) (complement has $\lambda=300$)
$S_9^{[2]}$ (>=1 isom. types)

1433 5-(19,8,168) (complement has $\lambda=196$)
TvT: 5-(18,7,36) $\cup$ 5-(18,8,132)

1485 5-(19,9,168) (complement has $\lambda=833$)
TvT: 5-(18,8,48) $\cup$ 5-(18,9,120) \cite{TranvanTrung86}

1673 5-(20,10,168) (complement has $\lambda=2835$)
Tran van Trung construction with supplementary design for design number 1670
Alltop construction for design number 1672
\cite{Krameretal85} $PSL(2,19)$ 1 isomorphism type

2991 5-(24,8,168) (complement has $\lambda=801$)
$PGL(2,23)$

3728 5-(25,10,168) (complement has $\lambda=15336$)
TvT: 5-(24,9,42) $\cup$ 5-(24,10,126)

5222 5-(33,7,168) (complement has $\lambda=210$)
\cite{Sebille98} $P\Gamma L(2,32)$

1273 5-(18,9,170) (complement has $\lambda=545$)
\cite{Brouwer86} $Hol(C_17)+$
Alltop construction for design number 1275

9619 5-(32,7,171) (complement has $\lambda=180$)
derived from number 9615

9615 6-(33,8,171) (complement has $\lambda=180$)
derived from number 9613

9613 7-(34,9,171) (complement has $\lambda=180$)
$P\Gamma L(2,32)+$ (many isomorphism types)

1199 5-(18,9,175) (complement has $\lambda=540$)
Alltop construction for design number 1196
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

1779 5-(20,8,175) (complement has $\lambda=280$)
\cite{Krameretal85} $PGL(2,19)$ 343 isomorphism types

2998 5-(24,8,176) (complement has $\lambda=793$)
$PGL(2,23)$

4775 5-(29,8,176) (complement has $\lambda=1848$)
TvT: 5-(28,7,22) $\cup$ 5-(28,8,154)

5341 5-(37,7,176) (complement has $\lambda=320$)
TvT: 5-(36,6,11) $\cup$ 5-(36,7,165)

941 5-(17,9,180) (complement has $\lambda=315$)
supplementary design of number 940

1277 5-(18,9,180) (complement has $\lambda=535$)
$PSL(2,17)$ 5 isomorphism types
Alltop construction for design number 1279
\cite{Kramer75}
\cite{Brouwer86} $Hol(C_17)+$

1946 5-(22,8,180) (complement has $\lambda=500$)
$PSL(2,19)++$

3517 5-(24,9,180) (complement has $\lambda=3696$)
$PGL(2,23)$ (>1 isomorphism types)

2433 5-(24,10,180) (complement has $\lambda=11448$)
$PSL(2,23)$ (45 isomorphism types) \cite{KitazumeMunemasa97}
\cite{Driessen78}

6302 5-(25,8,180) (complement has $\lambda=960$)
derived from number 6301

3879 5-(25,9,180) (complement has $\lambda=4665$)
TvT: 5-(24,8,36) $\cup$ 5-(24,9,144)

6301 6-(26,9,180) (complement has $\lambda=960$)
$PSL(2,25)$

1489 5-(19,9,182) (complement has $\lambda=819$)
TvT: 5-(18,8,52) $\cup$ 5-(18,9,130)

3006 5-(24,8,184) (complement has $\lambda=785$)
$PGL(2,23)$

1281 5-(18,9,185) (complement has $\lambda=530$)
$PSL(2,17)$ 1 isomorphism type
Alltop construction for design number 1283
\cite{Kramer75}

1496 5-(19,9,189) (complement has $\lambda=812$)
TvT: 5-(18,8,54) $\cup$ 5-(18,9,135)

1713 5-(20,10,189) (complement has $\lambda=2814$)
\cite{Krameretal85}
Alltop construction for design number 1715

3901 5-(26,10,189) (complement has $\lambda=20160$)
TvT: 5-(25,9,45) $\cup$ 5-(25,10,144)

1206 5-(18,9,190) (complement has $\lambda=525$)
Alltop construction for design number 1203
$PSL(2,8)\times C_2$ many isomorphism types
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,76))

5750 5-(23,8,192) (complement has $\lambda=624$)
residual design of number 5747
design of number 7849 with respect to smaller t

3730 5-(25,10,192) (complement has $\lambda=15312$)
TvT: 5-(24,9,48) $\cup$ 5-(24,10,144)

5464 5-(64,7,192) (complement has $\lambda=1519$)
$A\Sigma L(3,4)$ many solutions

936 5-(18,9,195) (complement has $\lambda=520$)
Tran van Trung construction with supplementary design for design number 933
Alltop construction for design number 935
\cite{Kramer75}
TvT: 5-(17,8,60) $\cup$ 5-(17,9,135) \cite{TranvanTrung86}
\cite{Brouwer86} Alltop(res(5-(18,8,78))
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

3881 5-(25,9,195) (complement has $\lambda=4650$)
TvT: 5-(24,8,39) $\cup$ 5-(24,9,156)

1503 5-(19,9,196) (complement has $\lambda=805$)
TvT: 5-(18,8,56) $\cup$ 5-(18,9,140)

5268 5-(34,7,196) (complement has $\lambda=210$)
$PGL(2,16)\times C_2$

2437 5-(24,10,198) (complement has $\lambda=11430$)
$PSL(2,23)$ (100 isomorphism types) \cite{KitazumeMunemasa97}

1215 5-(18,9,200) (complement has $\lambda=515$)
Alltop construction for design number 1212
\cite{Brouwer86} Alltop(res(5-(18,8,80))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

1949 5-(22,8,200) (complement has $\lambda=480$)
$PSL(2,19)++$
residual design of number 7856
derived from number 7882

7882 6-(23,9,200) (complement has $\lambda=480$)
residual design of number 7880

3018 5-(24,8,200) (complement has $\lambda=769$)
$PGL(2,23)$

4880 5-(30,8,200) (complement has $\lambda=2100$)
TvT: 5-(29,7,24) $\cup$ 5-(29,8,176)

6253 5-(24,8,204) (complement has $\lambda=765$)
residual design of number 6251

1222 5-(18,9,205) (complement has $\lambda=510$)
Alltop construction for design number 1219
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type
\cite{Brouwer86} Alltop(res(5-(18,8,82))

1229 5-(18,9,210) (complement has $\lambda=505$)
Alltop construction for design number 1226
$PSL(2,17)$ 1 isomorphism type
$PSL(2,8)\times C_2$ many isomorphism types
\cite{Kramer75}
\cite{Brouwer86} $Hol(C_17)+$

1517 5-(19,9,210) (complement has $\lambda=791$)
TvT: 5-(18,8,60) $\cup$ 5-(18,9,150) \cite{TranvanTrung86}

1440 5-(19,10,210) (complement has $\lambda=1792$)
supplementary design of number 1439

1781 5-(20,8,210) (complement has $\lambda=245$)
\cite{Krameretal85} $PGL(2,19)$ 644 isomorphism types

1792 5-(20,9,210) (complement has $\lambda=1155$)
TvT: 5-(19,8,56) $\cup$ 5-(19,9,154) \cite{TranvanTrung86}

1717 5-(20,10,210) (complement has $\lambda=2793$)
\cite{Krameretal85} $PSL(2,19)$ 101 isomorphism types
Alltop construction for design number 1719

1967 5-(22,9,210) (complement has $\lambda=2170$)
\cite{Kreher95} $PSL(2,19)++$
\cite{Kreher95}

3585 5-(24,9,210) (complement has $\lambda=3666$)
$PGL(2,23)$ (>1 isomorphism types)

3956 5-(26,8,210) (complement has $\lambda=1120$)
$PSL(2,25)$

1285 5-(18,9,215) (complement has $\lambda=500$)
$PSL(2,17)$ 2 isomorphism types
Alltop construction for design number 1287
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

10957 5-(23,8,216) (complement has $\lambda=600$)
TvT: 5-(22,7,36) $\cup$ 5-(22,8,180)

2448 5-(24,10,216) (complement has $\lambda=11412$)
$PGL(2,23)$ (3 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (185 isomorphism types) \cite{KitazumeMunemasa97}

3732 5-(25,10,216) (complement has $\lambda=15288$)
$PSL(2,23)+$ TvT construction 5-(24,9,54) $\cup$ 5-(24,10,162)

1524 5-(19,9,217) (complement has $\lambda=784$)
TvT: 5-(18,8,62) $\cup$ 5-(18,9,155) \cite{TranvanTrung86}

1289 5-(18,9,220) (complement has $\lambda=495$)
$PSL(2,17)$ 9 isomorphism types
Alltop construction for design number 1291
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type

1952 5-(22,8,220) (complement has $\lambda=460$)
$PSL(2,19)++$

4814 5-(30,12,220) (complement has $\lambda=480480$)
\cite{MacWilliamsetal78}

1528 5-(19,9,224) (complement has $\lambda=777$)
TvT: 5-(18,8,64) $\cup$ 5-(18,9,160) \cite{TranvanTrung86}

1447 5-(19,10,224) (complement has $\lambda=1778$)
supplementary design of number 1446

927 5-(17,9,225) (complement has $\lambda=270$)
supplementary design of number 926

1236 5-(18,9,225) (complement has $\lambda=490$)
Alltop construction for design number 1233
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

3891 5-(25,9,225) (complement has $\lambda=4620$)
TvT: 5-(24,8,45) $\cup$ 5-(24,9,180)

5748 5-(24,8,228) (complement has $\lambda=741$)
design of number 5747 with respect to smaller t

1243 5-(18,9,230) (complement has $\lambda=485$)
Alltop construction for design number 1240
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,92))

1532 5-(19,9,231) (complement has $\lambda=770$)
TvT: 5-(18,8,66) $\cup$ 5-(18,9,165) \cite{TranvanTrung86}

1721 5-(20,10,231) (complement has $\lambda=2772$)
\cite{Krameretal85} $PSL(2,19)$ 56 isomorphism types
Alltop construction for design number 1723

2452 5-(24,10,234) (complement has $\lambda=11394$)
$PSL(2,23)$ (248 isomorphism types) \cite{KitazumeMunemasa97}

1250 5-(18,9,235) (complement has $\lambda=480$)
Alltop construction for design number 1247
\cite{Brouwer86} Alltop(res(5-(18,8,94))
\cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

1257 5-(18,9,240) (complement has $\lambda=475$)
Alltop construction for design number 1254
$PSL(2,17)$ 1 isomorphism type
\cite{Brouwer86} Alltop(res(5-(18,8,96))
\cite{Kramer75} $PGL(2,16)+$ 4 isomorphism types

1956 5-(22,8,240) (complement has $\lambda=440$)
$PSL(2,19)++$
derived from number 7831
residual design of number 7861

5759 5-(23,8,240) (complement has $\lambda=576$)
residual design of number 5756
design of number 7856 with respect to smaller t
derived from number 7881

7831 6-(23,9,240) (complement has $\lambda=440$)
derived from number 7829
residual design of number 7884

3588 5-(24,9,240) (complement has $\lambda=3636$)
$PSL(2,23)$ (>1 isomorphism types)

7881 6-(24,9,240) (complement has $\lambda=576$)
design of number 7880 with respect to smaller t
residual design of number 7894

7829 7-(24,10,240) (complement has $\lambda=440$)
PGL(2,23) (>= 76 isom. types) \cite{Bettenetal97b}

6252 5-(25,8,240) (complement has $\lambda=900$)
design of number 6251 with respect to smaller t
derived from number 6306

3734 5-(25,10,240) (complement has $\lambda=15264$)
$PSL(2,23)+$ TvT construction 5-(24,9,60) $\cup$ 5-(24,10,180)

6306 6-(26,9,240) (complement has $\lambda=900$)
$PSL(2,25)$
derived from number 8009

8009 7-(27,10,240) (complement has $\lambda=900$)
$P\Gamma L(2,25)+$ \cite{Bettenetal97b}

5468 5-(64,7,240) (complement has $\lambda=1471$)
$A\Sigma L(3,4)$ many solutions

1264 5-(18,9,245) (complement has $\lambda=470$)
Alltop construction for design number 1261
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,98))

1536 5-(19,9,245) (complement has $\lambda=756$)
TvT: 5-(18,8,70) $\cup$ 5-(18,9,175)

7724 5-(37,7,248) (selfcomplementary)
residual design of number 7721
residual design of complement of number 7721
derived from number 7731
derived from complement of number 7731

7731 6-(38,8,248) (selfcomplementary)
\cite{Ajoodani94} using 6_(22,7,7) and 6_(22,8,60)

1293 5-(18,9,250) (complement has $\lambda=465$)
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
Alltop construction for design number 1295
\cite{Brouwer86} $Hol(C_17)+$

1725 5-(20,10,252) (complement has $\lambda=2751$)
\cite{Krameretal85} $PGL(2,19)$ 6 isomorphism types
Alltop construction for design number 1727

2261 5-(22,11,252) (complement has $\lambda=12124$)
$PGL(2,19)++$ 2 solutions
Alltop construction for design number 2263

3589 5-(24,9,252) (complement has $\lambda=3624$)
$PGL(2,23)$ (>1 isomorphism types)

2456 5-(24,10,252) (complement has $\lambda=11376$)
$PSL(2,23)$ (689 isomorphism types) \cite{KitazumeMunemasa97}

7204 5-(28,8,252) (complement has $\lambda=1519$)
residual design of number 7203
derived from number 7331

7331 6-(29,9,252) (complement has $\lambda=1519$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

1297 5-(18,9,255) (complement has $\lambda=460$)
\cite{Kramer75} $PGL(2,16)+$ 4 isomorphism types
Alltop construction for design number 1299
\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types

6258 5-(24,8,255) (complement has $\lambda=714$)
residual design of number 6256

3591 5-(24,9,258) (complement has $\lambda=3618$)
$PSL(2,23)$ (>1 isomorphism types)

943 5-(18,9,260) (complement has $\lambda=455$)
Tran van Trung construction with supplementary design for design number 940
Alltop construction for design number 942
TvT: 5-(17,8,80) $\cup$ 5-(17,9,180) \cite{TranvanTrung86}
\cite{Brouwer86} $Hol(C_17)+$
\cite{Brouwer86} Alltop(res(5-(18,8,104))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

3593 5-(24,9,264) (complement has $\lambda=3612$)
$PGL(2,23)$ (>1 isomorphism types)

3736 5-(25,10,264) (complement has $\lambda=15240$)
$PSL(2,23)+$ TvT construction 5-(24,9,66) $\cup$ 5-(24,10,198)

7722 5-(38,7,264) (selfcomplementary)
design of number 7721 with respect to smaller t
complementary design of number 7721 with respect to smaller t
derived from number 7737
derived from complement of number 7737

7737 6-(39,8,264) (selfcomplementary)
(6-(23+16m,8,4(m+1)(16m+17) m=1) \cite{Kreher93}

1301 5-(18,9,265) (complement has $\lambda=450$)
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types
Alltop construction for design number 1303

1543 5-(19,9,266) (complement has $\lambda=735$)
TvT: 5-(18,8,76) $\cup$ 5-(18,9,190) \cite{TranvanTrung86}

1454 5-(19,10,266) (complement has $\lambda=1736$)
supplementary design of number 1453

985 5-(18,9,270) (complement has $\lambda=445$)
Alltop construction for design number 982
\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,108))

2395 5-(23,9,270) (complement has $\lambda=2790$)
TvT: 5-(22,8,60) $\cup$ 5-(22,9,210)

2464 5-(24,10,270) (complement has $\lambda=11358$)
$PSL(2,23)$ (691 isomorphism types) \cite{KitazumeMunemasa97}

1547 5-(19,9,273) (complement has $\lambda=728$)
TvT: 5-(18,8,78) $\cup$ 5-(18,9,195) \cite{TranvanTrung86}

1729 5-(20,10,273) (complement has $\lambda=2730$)
\cite{Krameretal85} $PSL(2,19)$ 818 isomorphism types
Alltop construction for design number 1731

5451 5-(48,7,273) (complement has $\lambda=630$)
$PSL(2,47)$

991 5-(18,9,275) (complement has $\lambda=440$)
Alltop construction for design number 988
$PSL(2,17)$ 9 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,110))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

998 5-(18,9,280) (complement has $\lambda=435$)
Alltop construction for design number 995
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,112))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

1551 5-(19,9,280) (complement has $\lambda=721$)
TvT: 5-(18,8,80) $\cup$ 5-(18,9,200) \cite{TranvanTrung86}

1461 5-(19,10,280) (complement has $\lambda=1722$)
supplementary design of number 1460

5560 5-(21,8,280) (selfcomplementary)
residual design of number 5559
residual design of complement of number 5559
derived from number 5561
derived from complement of number 5561

1886 5-(21,9,280) (complement has $\lambda=1540$)
TvT: 5-(20,8,70) $\cup$ 5-(20,9,210) \cite{TranvanTrung86}

1960 5-(22,8,280) (complement has $\lambda=400$)
$PSL(2,19)++$
residual design of number 7868

1970 5-(22,9,280) (complement has $\lambda=2100$)
$PSL(2,19)++$

2265 5-(22,11,280) (complement has $\lambda=12096$)
\cite{Kreher95} $PGL(2,19)++$ 4 solutions
Alltop construction for design number 2267

5561 6-(22,9,280) (selfcomplementary)
$(PSL(3,2)\times S_3)+$ Halving of the complete design

3958 5-(26,8,280) (complement has $\lambda=1050$)
TvT: 5-(25,7,40) $\cup$ 5-(25,8,240)

7047 5-(27,8,280) (complement has $\lambda=1260$)
residual design of number 7045

4778 5-(29,8,280) (complement has $\lambda=1744$)
$PGL(2,27)+$ (>=1 isom. types)

3596 5-(24,9,282) (complement has $\lambda=3594$)
$PGL(2,23)$ (>1 isomorphism types)

1005 5-(18,9,285) (complement has $\lambda=430$)
Alltop construction for design number 1002
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type
\cite{Brouwer86} Alltop(res(5-(18,8,114))

5757 5-(24,8,285) (complement has $\lambda=684$)
design of number 5756 with respect to smaller t
derived from number 6275

6275 6-(25,9,285) (complement has $\lambda=684$)
\cite{Sebille98} $ AGL(2,5)$
design of number 7894 with respect to smaller t

5454 5-(49,7,286) (complement has $\lambda=660$)
TvT: 5-(48,6,13) $\cup$ 5-(48,7,273)

1558 5-(19,9,287) (complement has $\lambda=714$)
TvT: 5-(18,8,82) $\cup$ 5-(18,9,205) \cite{TranvanTrung86}

5766 5-(23,8,288) (complement has $\lambda=528$)
residual design of number 5763
design of number 7861 with respect to smaller t
derived from number 7885

3054 5-(24,8,288) (complement has $\lambda=681$)
$M_{11}_{12}\times id_2$

2468 5-(24,10,288) (complement has $\lambda=11340$)
$PGL(2,23)$ (4 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (1783 isomorphism types) \cite{KitazumeMunemasa97}

7885 6-(24,9,288) (complement has $\lambda=528$)
design of number 7884 with respect to smaller t
derived from number 7888
residual design of number 7895

3738 5-(25,10,288) (complement has $\lambda=15216$)
$PSL(2,23)+$ TvT construction 5-(24,9,72) $\cup$ 5-(24,10,216)

7888 7-(25,10,288) (complement has $\lambda=528$)
(Tran van Trung construction): 7-(24,9,48) together with 7-(24,10,240) \cite{Bettenetal97b}

4781 5-(29,8,288) (complement has $\lambda=1736$)
$PGL(2,27)+$ (>=1 isom. types)
design of number 7203 with respect to smaller t
derived from number 7555

7555 6-(30,9,288) (complement has $\lambda=1736$)
(Tran van Trung construction): 6-(29,8,36) together with 6-(29,9,252) \cite{Bettenetal97b}

364 5-(18,9,290) (complement has $\lambda=425$)
Alltop construction for design number 361
Alltop construction
residual design of number 7811
derived from number 7812

7812 6-(19,10,290) (complement has $\lambda=425$)
residual design of number 7810
supplementary design of number 7811

1562 5-(19,9,294) (complement has $\lambda=707$)
TvT: 5-(18,8,84) $\cup$ 5-(18,9,210)

1468 5-(19,10,294) (complement has $\lambda=1708$)
supplementary design of number 1467

1733 5-(20,10,294) (complement has $\lambda=2709$)
\cite{Krameretal85}
Alltop construction for design number 1735

7209 5-(28,8,294) (complement has $\lambda=1477$)
residual design of number 7206
derived from number 7337

7337 6-(29,9,294) (complement has $\lambda=1477$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

283 5-(49,7,294) (complement has $\lambda=652$)
$AGL(2,7)$

1012 5-(18,9,295) (complement has $\lambda=420$)
Alltop construction for design number 1009
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types

1309 5-(18,9,300) (complement has $\lambda=415$)
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type
Alltop construction for design number 1311
\cite{Brouwer86} $Hol(C_17)+$

6257 5-(25,8,300) (complement has $\lambda=840$)
design of number 6256 with respect to smaller t

829 5-(25,9,300) (complement has $\lambda=4545$)
TvT: 5-(24,8,60) $\cup$ 5-(24,9,240)

7643 5-(30,8,300) (complement has $\lambda=2000$)
derived from number 7641

7641 6-(31,9,300) (complement has $\lambda=2000$)
$PGL(3,5)$ (56 isom. types)

7664 5-(32,8,300) (complement has $\lambda=2625$)
residual design of number 7661

7217 5-(28,8,301) (complement has $\lambda=1470$)
residual design of number 7216

1019 5-(18,9,305) (complement has $\lambda=410$)
Alltop construction for design number 1016
$PSL(2,17)$ 6 isomorphism types
\cite{Kramer75}

6263 5-(24,8,306) (complement has $\lambda=663$)
residual design of number 6261
derived from number 8002

3599 5-(24,9,306) (complement has $\lambda=3570$)
$PGL(2,23)$ (>1 isomorphism types)

2476 5-(24,10,306) (complement has $\lambda=11322$)
$PSL(2,23)$ (2038 isomorphism types) \cite{KitazumeMunemasa97}

8002 6-(25,9,306) (complement has $\lambda=663$)
residual design of number 8001

86 5-(42,7,306) (complement has $\lambda=360$)
$PSL(3,4) \times C_2$ 3 solutions

5535 5-(19,9,308) (complement has $\lambda=693$)
residual design of number 5533

1353 5-(19,10,308) (complement has $\lambda=1694$)
TvT: 5-(18,9,110) $\cup$ 5-(18,10,198) \cite{TranvanTrung86}
supplementary design of number 1474

1999 5-(22,10,308) (complement has $\lambda=5880$)
$PGL(2,19)++$ 5 solutions

1026 5-(18,9,310) (complement has $\lambda=405$)
Alltop construction for design number 1023
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,124))
residual design of number 7818
derived from number 7819

7819 6-(19,10,310) (complement has $\lambda=405$)
residual design of number 7817
supplementary design of number 7818

3602 5-(24,9,312) (complement has $\lambda=3564$)
$PSL(2,23)$ (>1 isomorphism types)

3740 5-(25,10,312) (complement has $\lambda=15192$)
$PSL(2,23)+$ TvT construction 5-(24,9,78) $\cup$ 5-(24,10,234)

1033 5-(18,9,315) (complement has $\lambda=400$)
Alltop construction for design number 1030
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,126))
residual design of number 5527
derived from number 5528

1569 5-(19,9,315) (complement has $\lambda=686$)
TvT: 5-(18,8,90) $\cup$ 5-(18,9,225)

5528 6-(19,10,315) (complement has $\lambda=400$)
supplementary design of number 5527
residual design of number 5530

1794 5-(20,9,315) (complement has $\lambda=1050$)
\cite{Krameretal85} $PGL(2,19)$ 555 isomorphism types
derived from number 5576

1442 5-(20,10,315) (complement has $\lambda=2688$)
Tran van Trung construction with supplementary design for design number 1439
Alltop construction for design number 1441
\cite{Krameretal85} $PGL(2,19)$ 6 isomorphism types

5576 6-(21,10,315) (complement has $\lambda=1050$)
derived from number 5575

5575 7-(22,11,315) (complement has $\lambda=1050$)
$PGL(2,19)++$ 1 solution = 1 isomorphism type
Alltop construction for design number 5576
PGL(2,19)++ 1 isom. type

3893 5-(25,9,315) (complement has $\lambda=4530$)
TvT: 5-(24,8,63) $\cup$ 5-(24,9,252)

3980 5-(26,9,315) (complement has $\lambda=5670$)
$PGL(2,25)$

287 5-(49,7,316) (complement has $\lambda=630$)
$AGL(2,7)$

5472 5-(64,7,316) (complement has $\lambda=1395$)
$A\Sigma L(3,4)$ many solutions

1040 5-(18,9,320) (complement has $\lambda=395$)
Alltop construction for design number 1037
$PSL(2,17)$ 9 isomorphism types
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,128))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

7844 5-(22,8,320) (complement has $\lambda=360$)
derived from number 7839
residual design of number 7875

7839 6-(23,9,320) (complement has $\lambda=360$)
derived from number 7837
residual design of number 7886

7837 7-(24,10,320) (complement has $\lambda=360$)
PGL(2,23) (>= 2 isom. types) \cite{Bettenetal97b}

1576 5-(19,9,322) (complement has $\lambda=679$)
TvT: 5-(18,8,92) $\cup$ 5-(18,9,230) \cite{TranvanTrung86}

1479 5-(19,10,322) (complement has $\lambda=1680$)
supplementary design of number 1478

4401 5-(28,8,322) (complement has $\lambda=1449$)
Bluskov
design of number 7045 with respect to smaller t
derived from number 7343

7343 6-(29,9,322) (complement has $\lambda=1449$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

6280 5-(24,8,324) (complement has $\lambda=645$)
derived from number 6278

2480 5-(24,10,324) (complement has $\lambda=11304$)
$PGL(2,23)$ (2 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (3716 isomorphism types) \cite{KitazumeMunemasa97}

6278 6-(25,9,324) (complement has $\lambda=645$)
\cite{Sebille98} $ AGL(2,5)$

929 5-(18,9,325) (complement has $\lambda=390$)
Tran van Trung construction with supplementary design for design number 926
Alltop construction for design number 928
\cite{Kramer75}
\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types

1580 5-(19,9,329) (complement has $\lambda=672$)
TvT: 5-(18,8,94) $\cup$ 5-(18,9,235) \cite{TranvanTrung86}

1048 5-(18,9,330) (complement has $\lambda=385$)
Alltop construction for design number 1045
\cite{Kramer75} $PGL(2,17)$ 4 isomorphism types
\cite{Kramer75}
\cite{Brouwer86} $Hol(C_17)+$

1313 5-(18,9,335) (complement has $\lambda=380$)
$PSL(2,17)$ 4 isomorphism types
Alltop construction for design number 1315
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
residual design of number 7823
derived from number 7824

7824 6-(19,10,335) (complement has $\lambda=380$)
residual design of number 7822
supplementary design of number 7823

1584 5-(19,9,336) (complement has $\lambda=665$)
TvT: 5-(18,8,96) $\cup$ 5-(18,9,240) \cite{TranvanTrung86}

1356 5-(19,10,336) (complement has $\lambda=1666$)
TvT: 5-(18,9,120) $\cup$ 5-(18,10,216) \cite{TranvanTrung86}
supplementary design of number 1485

1449 5-(20,10,336) (complement has $\lambda=2667$)
Tran van Trung construction with supplementary design for design number 1446
Alltop construction for design number 1448
\cite{Krameretal85} $PSL(2,19)$ 89638 isomorphism types
$PSL(3,4)$

1826 5-(21,10,336) (complement has $\lambda=4032$)
$PSL(3,4)$ 1 isomorphism type
\cite{Kramer84} $PSL(2,19)+$ 9040 solutions
TvT: 5-(20,9,105) $\cup$ 5-(20,10,231) \cite{TranvanTrung86}

95 5-(22,11,336) (complement has $\lambda=12040$)
Alltop construction for design number 92
$PSL(3,4)+$ 3 isomorphism types
\cite{Kreher95}
PSL(3,4)+ Alltop construction from 4-(21,10,336)

5774 5-(23,8,336) (complement has $\lambda=480$)
residual design of number 5771
design of number 7868 with respect to smaller t

2676 5-(24,11,336) (complement has $\lambda=26796$)
\cite{Bluskov}

3742 5-(25,10,336) (complement has $\lambda=15168$)
$PSL(2,23)+$ TvT construction 5-(24,9,84) $\cup$ 5-(24,10,252)

7207 5-(29,8,336) (complement has $\lambda=1688$)
design of number 7206 with respect to smaller t
derived from number 7558

7558 6-(30,9,336) (complement has $\lambda=1688$)
(Tran van Trung construction): 6-(29,8,42) together with 6-(29,9,294) \cite{Bettenetal97b}

7662 5-(33,8,336) (complement has $\lambda=2940$)
design of number 7661 with respect to smaller t

1055 5-(18,9,340) (complement has $\lambda=375$)
Alltop construction for design number 1052
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
\cite{Kramer75} $PGL(2,16)+$ 4 isomorphism types

1964 5-(22,8,340) (selfcomplementary)
\cite{Kreher95} $PSL(2,19)++$
design of number 5559 with respect to smaller t
complementary design of number 5559 with respect to smaller t
residual design of number 5658
residual design of complement of number 5658
derived from number 5660
derived from complement of number 5660

5660 6-(23,9,340) (selfcomplementary)
derived 7-(24,10,340) Halving of the complete design
derived from number 7846
derived from complement of number 7846

7846 7-(24,10,340) (selfcomplementary)
PSL(2,23) (>= 1 isom. types) halving \cite{Laue98}

5764 5-(24,8,342) (complement has $\lambda=627$)
design of number 5763 with respect to smaller t
derived from number 7896

3604 5-(24,9,342) (complement has $\lambda=3534$)
$PGL(2,23)$ (>1 isomorphism types)

2484 5-(24,10,342) (complement has $\lambda=11286$)
$PSL(2,23)$ (4929 isomorphism types) \cite{KitazumeMunemasa97}

7896 6-(25,9,342) (complement has $\lambda=627$)
design of number 7895 with respect to smaller t
derived from number 7901

7901 7-(26,10,342) (complement has $\lambda=627$)
(Tran van Trung construction): 7-(25,9,54) together with 7-(25,10,288) \cite{Bettenetal97b}

1588 5-(19,9,343) (complement has $\lambda=658$)
TvT: 5-(18,8,98) $\cup$ 5-(18,9,245) \cite{TranvanTrung86}

7222 5-(28,8,343) (complement has $\lambda=1428$)
residual design of number 7219

4784 5-(29,8,344) (complement has $\lambda=1680$)
$PGL(2,27)+$ (>=1 isom. types)
design of number 7216 with respect to smaller t

1317 5-(18,9,345) (complement has $\lambda=370$)
\cite{Kramer75} $PGL(2,17)$ 4 isomorphism types
Alltop construction for design number 1319
\cite{Kramer75}

1069 5-(18,9,350) (complement has $\lambda=365$)
Alltop construction for design number 1066
$PSL(2,17)$ 2 isomorphism types
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,140))

5565 5-(21,9,350) (complement has $\lambda=1470$)
derived from number 5563

5563 6-(22,10,350) (complement has $\lambda=1470$)
$PSL(2,19)++$

3961 5-(26,8,350) (complement has $\lambda=980$)
TvT: 5-(25,7,50) $\cup$ 5-(25,8,300)

1076 5-(18,9,355) (complement has $\lambda=360$)
Alltop construction for design number 1073
\cite{Kramer75}
\cite{Brouwer86} Alltop(res(5-(18,8,142))
\cite{Kramer75} $PGL(2,16)+$ 4 isomorphism types
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

1737 5-(20,10,357) (complement has $\lambda=2646$)
\cite{Krameretal85} $PGL(2,19)$ 25 isomorphism types
Alltop construction for design number 1739

6267 5-(24,8,357) (complement has $\lambda=612$)
residual design of number 6265
derived from number 8004

8004 6-(25,9,357) (complement has $\lambda=612$)
residual design of number 8003

10958 5-(23,9,360) (complement has $\lambda=2700$)
TvT: 5-(22,8,80) $\cup$ 5-(22,9,280)

2492 5-(24,10,360) (complement has $\lambda=11268$)
$PGL(2,23)$ (3 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (8211 isomorphism types) \cite{KitazumeMunemasa97}

6262 5-(25,8,360) (complement has $\lambda=780$)
design of number 6261 with respect to smaller t
residual design of number 6295
derived from number 6309

3744 5-(25,10,360) (complement has $\lambda=15144$)
$PSL(2,23)+$ TvT construction 5-(24,9,90) $\cup$ 5-(24,10,270)

6309 6-(26,9,360) (complement has $\lambda=780$)
$PSL(2,25)$
design of number 8001 with respect to smaller t
residual design of number 8813

1592 5-(19,9,364) (complement has $\lambda=637$)
TvT: 5-(18,8,104) $\cup$ 5-(18,9,260) \cite{TranvanTrung86}

1490 5-(19,10,364) (complement has $\lambda=1638$)
supplementary design of number 1489

2269 5-(22,11,364) (complement has $\lambda=12012$)
$PGL(2,19)++$ 2 solutions
Alltop construction for design number 2271

5476 5-(64,7,364) (complement has $\lambda=1347$)
$A\Sigma L(3,4)$ many solutions

5025 5-(32,8,365) (complement has $\lambda=2560$)
$AGL(4,2)\times C_2$ 4 solutions

40 5-(29,8,368) (complement has $\lambda=1656$)
TvT: 5-(28,7,46) $\cup$ 5-(28,8,322)

3609 5-(24,9,372) (complement has $\lambda=3504$)
$PGL(2,23)$ (>1 isomorphism types)

1599 5-(19,9,378) (complement has $\lambda=623$)
TvT: 5-(18,8,108) $\cup$ 5-(18,9,270) \cite{TranvanTrung86}

1497 5-(19,10,378) (complement has $\lambda=1624$)
supplementary design of number 1496

1741 5-(20,10,378) (complement has $\lambda=2625$)
\cite{Krameretal85}
Alltop construction for design number 1743
\cite{Krameretal85} $PGL(2,19)$ 13 isomorphism types

2006 5-(22,10,378) (complement has $\lambda=5810$)
$PGL(2,19)++$ 126 solutions

2496 5-(24,10,378) (complement has $\lambda=11250$)
$PSL(2,23)$ (9082 isomorphism types) \cite{KitazumeMunemasa97}

3903 5-(26,10,378) (complement has $\lambda=19971$)
TvT: 5-(25,9,90) $\cup$ 5-(25,10,288)

5781 5-(23,8,384) (complement has $\lambda=432$)
residual design of number 5778
design of number 7875 with respect to smaller t
derived from number 7887

7887 6-(24,9,384) (complement has $\lambda=432$)
design of number 7886 with respect to smaller t
derived from number 7891
residual design of number 7898

3746 5-(25,10,384) (complement has $\lambda=15120$)
$PSL(2,23)+$ TvT construction 5-(24,9,96) $\cup$ 5-(24,10,288)

7891 7-(25,10,384) (complement has $\lambda=432$)
(Tran van Trung construction): 7-(24,9,64) together with 7-(24,10,320) \cite{Bettenetal97b}

1603 5-(19,9,385) (complement has $\lambda=616$)
TvT: 5-(18,8,110) $\cup$ 5-(18,9,275) \cite{TranvanTrung86}

4142 5-(27,9,385) (complement has $\lambda=6930$)
TvT: 5-(26,8,70) $\cup$ 5-(26,9,315)

5480 5-(64,7,388) (complement has $\lambda=1323$)
$A\Sigma L(3,4)$ many solutions

1607 5-(19,9,392) (complement has $\lambda=609$)
TvT: 5-(18,8,112) $\cup$ 5-(18,9,280) \cite{TranvanTrung86}

1504 5-(19,10,392) (complement has $\lambda=1610$)
supplementary design of number 1503

2013 5-(22,10,392) (complement has $\lambda=5796$)
$PGL(2,19)++$ 425 solutions

7220 5-(29,8,392) (complement has $\lambda=1632$)
design of number 7219 with respect to smaller t

3093 5-(24,8,393) (complement has $\lambda=576$)
$M_{11}_{12}\times id_2$

2500 5-(24,10,396) (complement has $\lambda=11232$)
$PGL(2,23)$ (2 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (15526 isomorphism types) \cite{KitazumeMunemasa97}

1611 5-(19,9,399) (complement has $\lambda=602$)
TvT: 5-(18,8,114) $\cup$ 5-(18,9,285) \cite{TranvanTrung86}

1456 5-(20,10,399) (complement has $\lambda=2604$)
Tran van Trung construction with supplementary design for design number 1453
Alltop construction for design number 1455
\cite{Krameretal85}

5772 5-(24,8,399) (complement has $\lambda=570$)
design of number 5771 with respect to smaller t

7232 5-(28,8,399) (complement has $\lambda=1372$)
residual design of number 7229

5029 5-(32,8,400) (complement has $\lambda=2525$)
$AGL(4,2)\times C_2$ 8 solutions

5033 5-(32,8,405) (complement has $\lambda=2520$)
$AGL(4,2)\times C_2$ 1 solution

5540 5-(19,9,406) (complement has $\lambda=595$)
derived from number 5539
design of number 7811 with respect to smaller t

5539 6-(20,10,406) (complement has $\lambda=595$)
$PSL(2,19)$ 7 isomorphism types
design of number 7810 with respect to smaller t
Tran van Trung construction with supplementary design for design number 7811

7350 5-(28,8,406) (complement has $\lambda=1365$)
derived from number 7348

7348 6-(29,9,406) (complement has $\lambda=1365$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

5659 5-(23,8,408) (selfcomplementary)
design of number 5658 with respect to smaller t
complementary design of number 5658 with respect to smaller t
derived from number 5787
derived from complement of number 5787

6272 5-(24,8,408) (complement has $\lambda=561$)
residual design of number 6270

5787 6-(24,9,408) (selfcomplementary)
TvT: 6-(23,8,68) $\cup$ 6-(23,9,340) Halving of the complete design

3748 5-(25,10,408) (complement has $\lambda=15096$)
TvT: 5-(24,9,102) $\cup$ 5-(24,10,306)

5484 5-(64,7,408) (complement has $\lambda=1303$)
$ASL(3,4)$ many solutions

1615 5-(19,9,413) (complement has $\lambda=588$)
TvT: 5-(18,8,118) $\cup$ 5-(18,9,295)

2504 5-(24,10,414) (complement has $\lambda=11214$)
$PSL(2,23)$ (14714 isomorphism types) \cite{KitazumeMunemasa97}

3750 5-(25,10,418) (complement has $\lambda=15086$)
$PSL(2,23)+$ TvT construction 5-(24,9,102) $\cup$ 5-(24,10,306)

1518 5-(19,10,420) (complement has $\lambda=1582$)
supplementary design of number 1517

1796 5-(20,9,420) (complement has $\lambda=945$)
\cite{Krameretal85} $PGL(2,19)$
design of number 5533 with respect to smaller t

1463 5-(20,10,420) (complement has $\lambda=2583$)
Tran van Trung construction with supplementary design for design number 1460
Alltop construction for design number 1462
\cite{Krameretal85} $PGL(2,19)$ 104 isomorphism types

1888 5-(21,9,420) (complement has $\lambda=1400$)
TvT: 5-(20,8,105) $\cup$ 5-(20,9,315) \cite{TranvanTrung86}

1973 5-(22,9,420) (complement has $\lambda=1960$)
$PSL(2,19)++$

2020 5-(22,10,420) (complement has $\lambda=5768$)
$PGL(2,19)++$ 183 solutions

6266 5-(25,8,420) (complement has $\lambda=720$)
design of number 6265 with respect to smaller t
residual design of number 6297
derived from number 6314

3964 5-(26,8,420) (complement has $\lambda=910$)
$PSL(2,25)$
design of number 6295 with respect to smaller t
derived from number 8814

6314 6-(26,9,420) (complement has $\lambda=720$)
$PSL(2,25)$
design of number 8003 with respect to smaller t

7051 5-(27,8,420) (complement has $\lambda=1120$)
residual design of number 7050
derived from number 9182

8814 6-(27,9,420) (complement has $\lambda=910$)
design of number 8813 with respect to smaller t

9182 6-(28,9,420) (complement has $\lambda=1120$)
derived from number 9180

9180 7-(29,10,420) (complement has $\lambda=1120$)
$P\Gamma L(2,27)+$ (>= 1 isom. types) \cite{Bettenetal97b}

5037 5-(32,8,420) (complement has $\lambda=2505$)
$AGL(4,2)\times C_2$ 6 solutions

5041 5-(32,8,425) (complement has $\lambda=2500$)
$AGL(4,2)\times C_2$ 5 solutions

1622 5-(19,9,427) (complement has $\lambda=574$)
TvT: 5-(18,8,122) $\cup$ 5-(18,9,305)

3113 5-(24,8,432) (complement has $\lambda=537$)
$M_{11}_{12}\times id_2$
derived from number 10488

3616 5-(24,9,432) (complement has $\lambda=3444$)
$PGL(2,23)$ (>1 isomorphism types)

2508 5-(24,10,432) (complement has $\lambda=11196$)
$PGL(2,23)$ (4 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (23725 isomorphism types) \cite{KitazumeMunemasa97}

3754 5-(25,10,432) (complement has $\lambda=15072$)
$PSL(2,23)+$ TvT construction 5-(24,9,108) $\cup$ 5-(24,10,324)

10488 6-(25,9,432) (complement has $\lambda=537$)
derived from number 10486

10486 7-(26,10,432) (complement has $\lambda=537$)
derived from number 10485

10485 8-(27,11,432) (complement has $\lambda=537$)
$ASL(3,3)$ (1 isom. type)

5545 5-(19,9,434) (complement has $\lambda=567$)
derived from number 5544
design of number 7818 with respect to smaller t

1359 5-(19,10,434) (complement has $\lambda=1568$)
TvT: 5-(18,9,155) $\cup$ 5-(18,10,279) \cite{TranvanTrung86}
supplementary design of number 1524

5544 6-(20,10,434) (complement has $\lambda=567$)
$PSL(2,19)$ 1 isomorphism type
design of number 7817 with respect to smaller t
Tran van Trung construction with supplementary design for design number 7818

5045 5-(32,8,440) (complement has $\lambda=2485$)
$AGL(4,2)\times C_2$ 2 solutions

1629 5-(19,9,441) (complement has $\lambda=560$)
TvT: 5-(18,8,126) $\cup$ 5-(18,9,315) \cite{TranvanTrung86}
design of number 5527 with respect to smaller t
derived from number 5529

1470 5-(20,10,441) (complement has $\lambda=2562$)
Tran van Trung construction with supplementary design for design number 1467
Alltop construction for design number 1469
\cite{Krameretal85} $PGL(2,19)$ 72 isomorphism types

5529 6-(20,10,441) (complement has $\lambda=560$)
Tran van Trung construction with supplementary design for design number 5527
design of number 5530 with respect to smaller t
$PSL(2,19)$ 4 isomorphism types

3905 5-(26,10,441) (complement has $\lambda=19908$)
TvT: 5-(25,9,105) $\cup$ 5-(25,10,336)

7242 5-(28,8,441) (complement has $\lambda=1330$)
residual design of number 7239

3620 5-(24,9,444) (complement has $\lambda=3432$)
$PGL(2,23)$ (>1 isomorphism types)

1633 5-(19,9,448) (complement has $\lambda=553$)
TvT: 5-(18,8,128) $\cup$ 5-(18,9,320) \cite{TranvanTrung86}

1362 5-(19,10,448) (complement has $\lambda=1554$)
TvT: 5-(18,9,160) $\cup$ 5-(18,10,288) \cite{TranvanTrung86}
supplementary design of number 1528

99 5-(22,11,448) (complement has $\lambda=11928$)
Alltop construction for design number 96
\cite{Kreher95} $PSL(3,4)+$ 1 isomorphism type, Alltop construction from 4-(21,10,448)

7251 5-(28,8,448) (complement has $\lambda=1323$)
residual design of number 7249
derived from number 7358

4787 5-(29,8,448) (complement has $\lambda=1576$)
$PGL(2,27)+$ (>=1 isom. types)

7358 6-(29,9,448) (complement has $\lambda=1323$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

2512 5-(24,10,450) (complement has $\lambda=11178$)
$PSL(2,23)$ (21430 isomorphism types) \cite{KitazumeMunemasa97}

1637 5-(19,9,455) (complement has $\lambda=546$)
TvT: 5-(18,8,130) $\cup$ 5-(18,9,325) \cite{TranvanTrung86}

4403 5-(28,8,455) (complement has $\lambda=1316$)
$A_8^{[2]}$ (>=1 isom. types)

5779 5-(24,8,456) (complement has $\lambda=513$)
design of number 5778 with respect to smaller t
derived from number 7899

10993 5-(24,9,456) (complement has $\lambda=3420$)
TvT: 5-(23,8,96) $\cup$ 5-(23,9,360)

3756 5-(25,10,456) (complement has $\lambda=15048$)
$PSL(2,23)+$ TvT construction 5-(24,9,114) $\cup$ 5-(24,10,342)

7899 6-(25,9,456) (complement has $\lambda=513$)
design of number 7898 with respect to smaller t
derived from number 7903

7903 7-(26,10,456) (complement has $\lambda=513$)
(Tran van Trung construction): 7-(25,9,72) together with 7-(25,10,384) \cite{Bettenetal97b}

7230 5-(29,8,456) (complement has $\lambda=1568$)
design of number 7229 with respect to smaller t

5488 5-(64,7,456) (complement has $\lambda=1255$)
$ASL(3,4)$ many solutions

6274 5-(24,8,459) (complement has $\lambda=510$)
residual design of number 6273
derived from number 8008

8008 6-(25,9,459) (complement has $\lambda=510$)
residual design of number 8007

5049 5-(32,8,460) (complement has $\lambda=2465$)
$AGL(4,2)\times C_2$ 37 solutions

1641 5-(19,9,462) (complement has $\lambda=539$)
TvT: 5-(18,8,132) $\cup$ 5-(18,9,330)

1365 5-(19,10,462) (complement has $\lambda=1540$)
TvT: 5-(18,9,165) $\cup$ 5-(18,10,297) \cite{TranvanTrung86}
supplementary design of number 1532

1476 5-(20,10,462) (complement has $\lambda=2541$)
Tran van Trung construction with supplementary design for design number 1474
Alltop construction for design number 1475
\cite{Krameretal85} $PSL(2,19)$
\cite{TranvanTrung86}

2027 5-(22,10,462) (complement has $\lambda=5726$)
$PGL(2,19)++$ 48 solutions

5053 5-(32,8,465) (complement has $\lambda=2460$)
$AGL(4,2)\times C_2$ 12 solutions

3624 5-(24,9,468) (complement has $\lambda=3408$)
$PGL(2,23)$ (>1 isomorphism types)

2516 5-(24,10,468) (complement has $\lambda=11160$)
$PSL(2,23)$ (30825 isomorphism types) \cite{KitazumeMunemasa97}

5549 5-(19,9,469) (complement has $\lambda=532$)
derived from number 5548
design of number 7823 with respect to smaller t

5548 6-(20,10,469) (complement has $\lambda=532$)
$PSL(2,19)$ 56 isomorphism types
design of number 7822 with respect to smaller t
Tran van Trung construction with supplementary design for design number 7823

7363 5-(28,8,469) (complement has $\lambda=1302$)
derived from number 7361

7361 6-(29,9,469) (complement has $\lambda=1302$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

1648 5-(19,9,476) (complement has $\lambda=525$)
TvT: 5-(18,8,136) $\cup$ 5-(18,9,340)

2034 5-(22,10,476) (complement has $\lambda=5712$)
\cite{Kreher95} $PGL(2,19)++$ 10 solutions
TvT: 5-(21,9,140) $\cup$ 5-(21,10,336)

4407 5-(28,8,476) (complement has $\lambda=1295$)
$A_8^{[2]}$ (>=1 isom. types)

6271 5-(25,8,480) (complement has $\lambda=660$)
design of number 6270 with respect to smaller t

3760 5-(25,10,480) (complement has $\lambda=15024$)
TvT: 5-(24,9,120) $\cup$ 5-(24,10,360)

3802 5-(25,11,480) (complement has $\lambda=38280$)
TvT: 5-(24,10,144) $\cup$ 5-(24,11,336)

9287 5-(29,8,480) (complement has $\lambda=1544$)
derived from number 9282

9282 6-(30,9,480) (complement has $\lambda=1544$)
derived from number 9280

9280 7-(31,10,480) (complement has $\lambda=1544$)
$PSL(3,5)$ ( >=1 isom. types)

1481 5-(20,10,483) (complement has $\lambda=2520$)
Tran van Trung construction with supplementary design for design number 1478
Alltop construction for design number 1480
\cite{Krameretal85} $PGL(2,19)$ 173 isomorphism types

30 5-(28,8,483) (complement has $\lambda=1288$)
residual design of number 28
Bluskov
design of number 7050 with respect to smaller t
derived from number 7371

7371 6-(29,9,483) (complement has $\lambda=1288$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

2520 5-(24,10,486) (complement has $\lambda=11142$)
$PSL(2,23)$ (26361 isomorphism types) \cite{KitazumeMunemasa97}

1662 5-(19,9,490) (complement has $\lambda=511$)
TvT: 5-(18,8,140) $\cup$ 5-(18,9,350) \cite{TranvanTrung86}

1537 5-(19,10,490) (complement has $\lambda=1512$)
supplementary design of number 1536

1976 5-(22,9,490) (complement has $\lambda=1890$)
$PSL(2,19)++$

6298 5-(26,8,490) (complement has $\lambda=840$)
design of number 6297 with respect to smaller t
derived from number 6831

6831 6-(27,9,490) (complement has $\lambda=840$)
TvT: 6-(26,8,70) $\cup$ 6-(26,9,420)
\cite{Sebille98} $P\Gamma L(2,25)$

7257 5-(28,8,490) (complement has $\lambda=1281$)
residual design of number 7254

3631 5-(24,9,492) (complement has $\lambda=3384$)
$PSL(2,23)$

1666 5-(19,9,497) (complement has $\lambda=504$)
TvT: 5-(18,8,142) $\cup$ 5-(18,9,355) \cite{TranvanTrung86}

5057 5-(32,8,500) (complement has $\lambda=2425$)
$AGL(4,2)\times C_2$ 118 solutions

1487 5-(20,10,504) (complement has $\lambda=2499$)
Tran van Trung construction with supplementary design for design number 1485
Alltop construction for design number 1486
\cite{Krameretal85}
\cite{TranvanTrung86}

2273 5-(22,11,504) (complement has $\lambda=11872$)
$PGL(2,19)++$
Alltop construction for design number 2275

3635 5-(24,9,504) (complement has $\lambda=3372$)
$PGL(2,23)$ (>1 isomorphism types)

2524 5-(24,10,504) (complement has $\lambda=11124$)
$PGL(2,23)$ (6 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (42919 isomorphism types) \cite{KitazumeMunemasa97}

3762 5-(25,10,504) (complement has $\lambda=15000$)
TvT: 5-(24,9,126) $\cup$ 5-(24,10,378)

3907 5-(26,10,504) (complement has $\lambda=19845$)
TvT: 5-(25,9,120) $\cup$ 5-(25,10,384)

7374 5-(28,8,504) (complement has $\lambda=1267$)
derived from number 7372

7240 5-(29,8,504) (complement has $\lambda=1520$)
design of number 7239 with respect to smaller t

7372 6-(29,9,504) (complement has $\lambda=1267$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

5061 5-(32,8,505) (complement has $\lambda=2420$)
$AGL(4,2)\times C_2$ 95 solutions

4411 5-(28,8,511) (complement has $\lambda=1260$)
$A_8^{[2]}$ (>=1 isom. types)

4791 5-(29,8,512) (complement has $\lambda=1512$)
$PGL(2,27)+$ (>=1 isom. types)
design of number 7249 with respect to smaller t
derived from number 7561

7561 6-(30,9,512) (complement has $\lambda=1512$)
(Tran van Trung construction): 6-(29,8,64) together with 6-(29,9,448) \cite{Bettenetal97b}

2036 5-(22,10,518) (complement has $\lambda=5670$)
$PGL(2,19)++$ 1535 solutions

9557 5-(31,8,520) (complement has $\lambda=2080$)
residual design of number 9551
derived from number 9552

9552 6-(32,9,520) (complement has $\lambda=2080$)
residual design of number 9549

7814 5-(18,10,522) (complement has $\lambda=765$)
residual design of number 7812

2528 5-(24,10,522) (complement has $\lambda=11106$)
$PSL(2,23)$ (27825 isomorphism types) \cite{KitazumeMunemasa97}

1798 5-(20,9,525) (complement has $\lambda=840$)
TvT: 5-(19,8,140) $\cup$ 5-(19,9,385) \cite{TranvanTrung86}
TvT: 5-(19,8,140) $\cup$ 5-(19,9,385) \cite{TranvanTrung86}
\cite{TranvanTrung86}

1745 5-(20,10,525) (complement has $\lambda=2478$)
\cite{Krameretal85} $PSL(2,19)$
Alltop construction for design number 1747

7310 5-(28,9,525) (complement has $\lambda=8330$)
residual design of number 7307

5065 5-(32,8,525) (complement has $\lambda=2400$)
$AGL(4,2)\times C_2$ 6 solutions

3764 5-(25,10,528) (complement has $\lambda=14976$)
TvT: 5-(24,9,132) $\cup$ 5-(24,10,396)

5492 5-(64,7,528) (complement has $\lambda=1183$)
$ASL(3,4)$ many solutions

1368 5-(19,10,532) (complement has $\lambda=1470$)
TvT: 5-(18,9,190) $\cup$ 5-(18,10,342) \cite{TranvanTrung86}
supplementary design of number 1543

7380 5-(28,8,532) (complement has $\lambda=1239$)
derived from number 7378

7378 6-(29,9,532) (complement has $\lambda=1239$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

10825 5-(23,9,540) (complement has $\lambda=2520$)
TvT: 5-(22,8,120) $\cup$ 5-(22,9,420)

2536 5-(24,10,540) (complement has $\lambda=11088$)
$PSL(2,23)$ (52255 isomorphism types) \cite{KitazumeMunemasa97}
\cite{Driessen78}

276 5-(25,8,540) (complement has $\lambda=600$)
derived from number 274
design of number 6273 with respect to smaller t

8019 5-(25,9,540) (complement has $\lambda=4305$)
derived from number 8017

3983 5-(26,9,540) (complement has $\lambda=5445$)
$PGL(2,25)$

274 6-(26,9,540) (complement has $\lambda=600$)
derived from number 273
$PSL(2,25)$
design of number 8007 with respect to smaller t

8017 6-(26,10,540) (complement has $\lambda=4305$)
derived from number 8016

273 7-(27,10,540) (complement has $\lambda=600$)
$ASL(3,3)^{13}$
$P\Gamma L(2,25)+$ \cite{Bettenetal97b}

8016 7-(27,11,540) (complement has $\lambda=4305$)
$ASL(3,3)$ 1 isomorphism type

5069 5-(32,8,540) (complement has $\lambda=2385$)
$AGL(4,2)\times C_2$ 174 solutions

5073 5-(32,8,545) (complement has $\lambda=2380$)
$AGL(4,2)\times C_2$ 70 solutions

1371 5-(19,10,546) (complement has $\lambda=1456$)
TvT: 5-(18,9,195) $\cup$ 5-(18,10,351) \cite{TranvanTrung86}
supplementary design of number 1547

1492 5-(20,10,546) (complement has $\lambda=2457$)
Tran van Trung construction with supplementary design for design number 1489
Alltop construction for design number 1491
\cite{Krameretal85} $PGL(2,19)$ 307 isomorphism types

2043 5-(22,10,546) (complement has $\lambda=5642$)
$PGL(2,19)++$

7267 5-(28,8,546) (complement has $\lambda=1225$)
residual design of number 7264

3766 5-(25,10,552) (complement has $\lambda=14952$)
TvT: 5-(24,9,138) $\cup$ 5-(24,10,414)

16 5-(29,8,552) (complement has $\lambda=1472$)
TvT: 5-(28,7,69) $\cup$ 5-(28,8,483)
design of number 28 with respect to smaller t
derived from number 34

34 6-(30,9,552) (complement has $\lambda=1472$)
TvT: 6-(29,8,69) $\cup$ 6-(29,9,483)

7820 5-(18,10,558) (complement has $\lambda=729$)
residual design of number 7819

2556 5-(24,10,558) (complement has $\lambda=11070$)
$PSL(2,23)$ (27210 isomorphism types) \cite{KitazumeMunemasa97}

1552 5-(19,10,560) (complement has $\lambda=1442$)
supplementary design of number 1551

1890 5-(21,9,560) (complement has $\lambda=1260$)
TvT: 5-(20,8,140) $\cup$ 5-(20,9,420)

2049 5-(22,10,560) (complement has $\lambda=5628$)
$PGL(2,19)++$

3968 5-(26,8,560) (complement has $\lambda=770$)
$PSL(2,25)$
TvT: 5-(25,7,80) $\cup$ 5-(25,8,480)

7055 5-(27,8,560) (complement has $\lambda=980$)
residual design of number 7053

4418 5-(28,8,560) (complement has $\lambda=1211$)
$A_8^{[2]}$ (>=1 isom. types)

7255 5-(29,8,560) (complement has $\lambda=1464$)
design of number 7254 with respect to smaller t

5077 5-(32,8,560) (complement has $\lambda=2365$)
$AGL(4,2)\times C_2$ 343 solutions

10472 5-(38,8,560) (complement has $\lambda=4896$)
derived from number 10467

10467 6-(39,9,560) (complement has $\lambda=4896$)
derived from number 10465

10465 7-(40,10,560) (complement has $\lambda=4896$)
$PSL(4,3)$ (many isomorphism types)

5081 5-(32,8,565) (complement has $\lambda=2360$)
$AGL(4,2)\times C_2$ 190 solutions

5531 5-(18,10,567) (complement has $\lambda=720$)
residual design of number 5528

1499 5-(20,10,567) (complement has $\lambda=2436$)
Tran van Trung construction with supplementary design for design number 1496
Alltop construction for design number 1498
\cite{Krameretal85} $PGL(2,19)$ 567 isomorphism types

3909 5-(26,10,567) (complement has $\lambda=19782$)
TvT: 5-(25,9,135) $\cup$ 5-(25,10,432)

4798 5-(29,8,568) (complement has $\lambda=1456$)
$PGL(2,27)+$ (>=1 isom. types)

1374 5-(19,10,574) (complement has $\lambda=1428$)
TvT: 5-(18,9,205) $\cup$ 5-(18,10,369) \cite{TranvanTrung86}
supplementary design of number 1558

2572 5-(24,10,576) (complement has $\lambda=11052$)
$PGL(2,23)$ (6 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (41169 isomorphism types) \cite{KitazumeMunemasa97}

2726 5-(24,12,576) (complement has $\lambda=49812$)
$PSL(2,23)$ (1 isomorphism type) \cite{AssmusMattson69c}
Alltop construction for design number 2728

3768 5-(25,10,576) (complement has $\lambda=14928$)
TvT: 5-(24,9,144) $\cup$ 5-(24,10,432)

5496 5-(64,7,576) (complement has $\lambda=1135$)
$ASL(3,4)$ many solutions

5085 5-(32,8,580) (complement has $\lambda=2345$)
$AGL(4,2)\times C_2$ 165 solutions

9554 5-(32,8,585) (complement has $\lambda=2340$)
derived from number 9550
design of number 9551 with respect to smaller t

9550 6-(33,9,585) (complement has $\lambda=2340$)
design of number 9549 with respect to smaller t

1563 5-(19,10,588) (complement has $\lambda=1414$)
supplementary design of number 1562

1506 5-(20,10,588) (complement has $\lambda=2415$)
Tran van Trung construction with supplementary design for design number 1503
Alltop construction for design number 1505
\cite{Krameretal85} $PSL(2,19)$

2056 5-(22,10,588) (complement has $\lambda=5600$)
$PGL(2,19)++$

7277 5-(28,8,588) (complement has $\lambda=1183$)
residual design of number 7274

2583 5-(24,10,594) (complement has $\lambda=11034$)
$PSL(2,23)$ (23963 isomorphism types) \cite{KitazumeMunemasa97}

4422 5-(28,8,595) (complement has $\lambda=1176$)
$A_8^{[2]}$ (>=1 isom. types)
residual design of number 7284
derived from number 7384

7384 6-(29,9,595) (complement has $\lambda=1176$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

3770 5-(25,10,600) (complement has $\lambda=14904$)
TvT: 5-(24,9,150) $\cup$ 5-(24,10,450)

9351 5-(31,8,600) (complement has $\lambda=2000$)
derived from number 9346

5089 5-(32,8,600) (complement has $\lambda=2325$)
$AGL(4,2)\times C_2$ 897 solutions

9346 6-(32,9,600) (complement has $\lambda=2000$)
derived from number 9344

9344 7-(33,10,600) (complement has $\lambda=2000$)
$P\Gamma L(2,32)$ (many isomorphism types)

2063 5-(22,10,602) (complement has $\lambda=5586$)
$PGL(2,19)++$

7826 5-(18,10,603) (complement has $\lambda=684$)
residual design of number 7824

5093 5-(32,8,605) (complement has $\lambda=2320$)
$AGL(4,2)\times C_2$ 4638 solutions

1749 5-(20,10,609) (complement has $\lambda=2394$)
\cite{Krameretal85}
Alltop construction for design number 1751

2587 5-(24,10,612) (complement has $\lambda=11016$)
$PGL(2,23)$ (3 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (26131 isomorphism types) \cite{KitazumeMunemasa97}

5537 5-(19,10,616) (complement has $\lambda=1386$)
supplementary design of number 5535

1827 5-(21,11,616) (complement has $\lambda=7392$)
supplementary design of number 1826

2005 5-(22,11,616) (complement has $\lambda=11760$)
Alltop construction for design number 2002

4426 5-(28,8,616) (complement has $\lambda=1155$)
$A_8^{[2]}$ (>=1 isom. types)

2681 5-(24,12,624) (complement has $\lambda=49764$)
Alltop construction for design number 2678

3772 5-(25,10,624) (complement has $\lambda=14880$)
TvT: 5-(24,9,156) $\cup$ 5-(24,10,468)

7265 5-(29,8,624) (complement has $\lambda=1400$)
design of number 7264 with respect to smaller t

1570 5-(19,10,630) (complement has $\lambda=1372$)
supplementary design of number 1569

1800 5-(20,9,630) (complement has $\lambda=735$)
\cite{Krameretal85} $PGL(2,19)$
derived from number 5581

1520 5-(20,10,630) (complement has $\lambda=2373$)
Tran van Trung construction with supplementary design for design number 1517
Alltop construction for design number 1519
\cite{Krameretal85} $PGL(2,19)$ 2106 isomorphism types

1892 5-(21,9,630) (complement has $\lambda=1190$)
$PSL(3,2)\times S_3$

5581 6-(21,10,630) (complement has $\lambda=735$)
derived from number 5580

1979 5-(22,9,630) (complement has $\lambda=1750$)
$PSL(2,19)++$

2070 5-(22,10,630) (complement has $\lambda=5558$)
$PGL(2,19)++$

5580 7-(22,11,630) (complement has $\lambda=735$)
$PGL(2,19)++$ 30 solutions
Alltop construction for design number 5581
PSL(2,19)++ (>= 1 isom. types)

10959 5-(23,9,630) (complement has $\lambda=2430$)
TvT: 5-(22,8,140) $\cup$ 5-(22,9,490)

2591 5-(24,10,630) (complement has $\lambda=10998$)
$PSL(2,23)$ (16889 isomorphism types) \cite{KitazumeMunemasa97}

3971 5-(26,8,630) (complement has $\lambda=700$)
$PSL(2,25)$
derived from number 8819

3987 5-(26,9,630) (complement has $\lambda=5355$)
$PGL(2,25)$

3913 5-(26,10,630) (complement has $\lambda=19719$)
TvT: 5-(25,9,150) $\cup$ 5-(25,10,480)

8819 6-(27,9,630) (complement has $\lambda=700$)
derived from number 8817

7387 5-(28,8,630) (complement has $\lambda=1141$)
derived from number 7385

7317 5-(28,9,630) (complement has $\lambda=8225$)
residual design of number 7314

8817 7-(28,10,630) (complement has $\lambda=700$)
$P\Gamma L(2,27)$ (>= 100 isom. types) \cite{Bettenetal97b}

7308 5-(29,9,630) (complement has $\lambda=9996$)
design of number 7307 with respect to smaller t

7385 6-(29,9,630) (complement has $\lambda=1141$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

7293 5-(28,8,637) (complement has $\lambda=1134$)
residual design of number 7290

9576 5-(31,8,640) (complement has $\lambda=1960$)
residual design of number 9570
derived from number 9571

5097 5-(32,8,640) (complement has $\lambda=2285$)
$AGL(4,2)\times C_2$ many solutions

9571 6-(32,9,640) (complement has $\lambda=1960$)
residual design of number 9568

1377 5-(19,10,644) (complement has $\lambda=1358$)
TvT: 5-(18,9,230) $\cup$ 5-(18,10,414) \cite{TranvanTrung86}
supplementary design of number 1576

4430 5-(28,8,644) (complement has $\lambda=1127$)
Bluskov
design of number 7053 with respect to smaller t

5101 5-(32,8,645) (complement has $\lambda=2280$)
$AGL(4,2)\times C_2$ many solutions

2595 5-(24,10,648) (complement has $\lambda=10980$)
$PGL(2,23)$ (3 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (19357 isomorphism types) \cite{KitazumeMunemasa97}

1526 5-(20,10,651) (complement has $\lambda=2352$)
Tran van Trung construction with supplementary design for design number 1524
Alltop construction for design number 1525
\cite{Krameretal85} $PSL(2,19)$
\cite{TranvanTrung86}

10660 5-(28,8,651) (complement has $\lambda=1120$)
residual design of number 10657
derived from number 10658

10658 6-(29,9,651) (complement has $\lambda=1120$)
residual design of number 10655
derived from number 10656

10656 7-(30,10,651) (complement has $\lambda=1120$)
residual design of number 10654

5500 5-(64,7,651) (complement has $\lambda=1060$)
$A\Sigma L(3,4)$ many solutions

1380 5-(19,10,658) (complement has $\lambda=1344$)
TvT: 5-(18,9,235) $\cup$ 5-(18,10,423) \cite{TranvanTrung86}
supplementary design of number 1580

5105 5-(32,8,665) (complement has $\lambda=2260$)
$AGL(4,2)\times C_2$ many solutions

2599 5-(24,10,666) (complement has $\lambda=10962$)
$PSL(2,23)$ (10178 isomorphism types) \cite{KitazumeMunemasa97}

1383 5-(19,10,672) (complement has $\lambda=1330$)
TvT: 5-(18,9,240) $\cup$ 5-(18,10,432) \cite{TranvanTrung86}
supplementary design of number 1584

1530 5-(20,10,672) (complement has $\lambda=2331$)
Tran van Trung construction with supplementary design for design number 1528
Alltop construction for design number 1529
\cite{Krameretal85} $PGL(2,19)$ 3994 isomorphism types
\cite{TranvanTrung86}

1833 5-(21,10,672) (complement has $\lambda=3696$)
TvT: 5-(20,9,210) $\cup$ 5-(20,10,462) \cite{TranvanTrung86}

2077 5-(22,10,672) (complement has $\lambda=5516$)
\cite{Kreher95} $PGL(2,19)++$

464 5-(22,11,672) (complement has $\lambda=11704$)
Alltop construction for design number 461
$PSL(3,4)+$ 9 isomorphism types
\cite{Kreher95} $PGL(2,19)++$ 1 isomorphism type
PSL(3,4)+ Alltop construction from 4-(21,10,672)

3933 5-(26,11,672) (complement has $\lambda=53592$)
TvT: 5-(25,10,192) $\cup$ 5-(25,11,480)

7397 5-(28,8,672) (complement has $\lambda=1099$)
derived from number 7395

7275 5-(29,8,672) (complement has $\lambda=1352$)
design of number 7274 with respect to smaller t

7395 6-(29,9,672) (complement has $\lambda=1099$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

8032 5-(25,9,675) (complement has $\lambda=4170$)
derived from number 8027

8027 6-(26,10,675) (complement has $\lambda=4170$)
derived from number 8025

8025 7-(27,11,675) (complement has $\lambda=4170$)
$ASL(3,3)$ 24 isomorphism types

5109 5-(32,8,675) (complement has $\lambda=2250$)
TvT: 5-(31,7,75) $\cup$ 5-(31,8,600)

5504 5-(64,7,675) (complement has $\lambda=1036$)
$A\Sigma L(3,4)$ many solutions

7285 5-(29,8,680) (complement has $\lambda=1344$)
design of number 7284 with respect to smaller t
derived from number 7564

7564 6-(30,9,680) (complement has $\lambda=1344$)
(Tran van Trung construction): 6-(29,8,85) together with 6-(29,9,595) \cite{Bettenetal97b}

9596 5-(31,8,680) (complement has $\lambda=1920$)
residual design of number 9590
derived from number 9591

5113 5-(32,8,680) (complement has $\lambda=2245$)
$AGL(4,2)\times C_2$ many solutions

9591 6-(32,9,680) (complement has $\lambda=1920$)
residual design of number 9588

2603 5-(24,10,684) (complement has $\lambda=10944$)
$PGL(2,23)$ (4 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (12572 isomorphism types) \cite{KitazumeMunemasa97}

5117 5-(32,8,685) (complement has $\lambda=2240$)
$AGL(4,2)\times C_2$ many solutions

1386 5-(19,10,686) (complement has $\lambda=1316$)
TvT: 5-(18,9,245) $\cup$ 5-(18,10,441) \cite{TranvanTrung86}
supplementary design of number 1588

2084 5-(22,10,686) (complement has $\lambda=5502$)
$PGL(2,19)++$

1534 5-(20,10,693) (complement has $\lambda=2310$)
Tran van Trung construction with supplementary design for design number 1532
Alltop construction for design number 1533
\cite{Krameretal85} $PGL(2,19)$ 3968 isomorphism types
residual design of number 5576
derived from number 5577

5577 6-(21,11,693) (complement has $\lambda=2310$)
residual design of number 5575
supplementary design of number 5576

7303 5-(28,8,693) (complement has $\lambda=1078$)
residual design of number 7300
derived from number 7401

7401 6-(29,9,693) (complement has $\lambda=1078$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

3652 5-(24,9,696) (complement has $\lambda=3180$)
$PSL(2,23)$

1895 5-(21,9,700) (complement has $\lambda=1120$)
TvT: 5-(20,8,175) $\cup$ 5-(20,9,525) \cite{TranvanTrung86}

1982 5-(22,9,700) (complement has $\lambda=1680$)
$PSL(2,19)++$
residual design of number 7882

7041 5-(27,8,700) (complement has $\lambda=840$)
residual design of number 7039

4434 5-(28,8,700) (complement has $\lambda=1071$)
$A_8^{[2]}$ (>=1 isom. types)
residual design of number 10647
derived from number 10648

10648 6-(29,9,700) (complement has $\lambda=1071$)
residual design of number 10645
derived from number 10646

10646 7-(30,10,700) (complement has $\lambda=1071$)
residual design of number 10644

5121 5-(32,8,700) (complement has $\lambda=2225$)
$AGL(4,2)\times C_2$

5238 5-(33,8,700) (complement has $\lambda=2576$)
\cite{Sebille98} $P\Gamma L(2,32)$

3654 5-(24,9,702) (complement has $\lambda=3174$)
$PSL(2,23)$

2607 5-(24,10,702) (complement has $\lambda=10926$)
$PSL(2,23)$ (6096 isomorphism types) \cite{KitazumeMunemasa97}

5125 5-(32,8,705) (complement has $\lambda=2220$)
$AGL(4,2)\times C_2$

1753 5-(20,10,714) (complement has $\lambda=2289$)
\cite{Krameretal85} $PGL(2,19)$
Alltop construction for design number 1755

3658 5-(24,9,714) (complement has $\lambda=3162$)
$PSL(2,23)$

2615 5-(24,10,720) (complement has $\lambda=10908$)
$PGL(2,23)$ (1 isomorphism type) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (5975 isomorphism types) \cite{KitazumeMunemasa97}

3774 5-(25,10,720) (complement has $\lambda=14784$)
TvT: 5-(24,9,180) $\cup$ 5-(24,10,540)

9367 5-(31,8,720) (complement has $\lambda=1880$)
derived from number 9362

9573 5-(32,8,720) (complement has $\lambda=2205$)
derived from number 9569
design of number 9570 with respect to smaller t

9362 6-(32,9,720) (complement has $\lambda=1880$)
derived from number 9360

9569 6-(33,9,720) (complement has $\lambda=2205$)
design of number 9568 with respect to smaller t

9360 7-(33,10,720) (complement has $\lambda=1880$)
$P\Gamma L(2,32)$ (many isomorphism types)

5508 5-(64,7,723) (complement has $\lambda=988$)
$A\Sigma L(3,4)$ many solutions

1593 5-(19,10,728) (complement has $\lambda=1274$)
supplementary design of number 1592

2091 5-(22,10,728) (complement has $\lambda=5460$)
$PGL(2,19)++$

7291 5-(29,8,728) (complement has $\lambda=1296$)
design of number 7290 with respect to smaller t

3664 5-(24,9,732) (complement has $\lambda=3144$)
$PSL(2,23)$

1539 5-(20,10,735) (complement has $\lambda=2268$)
Tran van Trung construction with supplementary design for design number 1536
Alltop construction for design number 1538
\cite{Krameretal85} $PGL(2,19)$

7166 5-(28,8,735) (complement has $\lambda=1036$)
residual design of number 7163
derived from number 7407

7407 6-(29,9,735) (complement has $\lambda=1036$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}
residual design of number 9278

2618 5-(24,10,738) (complement has $\lambda=10890$)
$PSL(2,23)$ (3105 isomorphism types) \cite{KitazumeMunemasa97}

7175 5-(28,8,742) (complement has $\lambda=1029$)
residual design of number 7172

3668 5-(24,9,744) (complement has $\lambda=3132$)
$PSL(2,23)$

9306 5-(29,8,744) (complement has $\lambda=1280$)
derived from number 9301
design of number 10657 with respect to smaller t

9301 6-(30,9,744) (complement has $\lambda=1280$)
derived from number 9299
design of number 10655 with respect to smaller t

9299 7-(31,10,744) (complement has $\lambda=1280$)
$PSL(3,5)$ ( >=1 isom. types)
design of number 10654 with respect to smaller t

5512 5-(64,7,744) (complement has $\lambda=967$)
$ASL(3,4)$ many solutions

3672 5-(24,9,750) (complement has $\lambda=3126$)
$PSL(2,23)$

4888 5-(30,9,750) (complement has $\lambda=11900$)
TvT: 5-(29,8,120) $\cup$ 5-(29,9,630)

1389 5-(19,10,756) (complement has $\lambda=1246$)
TvT: 5-(18,9,270) $\cup$ 5-(18,10,486) \cite{TranvanTrung86}
supplementary design of number 1599

1757 5-(20,10,756) (complement has $\lambda=2247$)
\cite{Krameretal85}
Alltop construction for design number 1759
\cite{Krameretal85} $PGL(2,19)$

2093 5-(22,10,756) (complement has $\lambda=5432$)
$PGL(2,19)++$

2012 5-(22,11,756) (complement has $\lambda=11620$)
Alltop construction for design number 2009

10827 5-(23,10,756) (complement has $\lambda=7812$)
TvT: 5-(22,9,210) $\cup$ 5-(22,10,546)

2622 5-(24,10,756) (complement has $\lambda=10872$)
$PGL(2,23)$ (1 isomorphism type) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (2341 isomorphism types) \cite{KitazumeMunemasa97}

3915 5-(26,10,756) (complement has $\lambda=19593$)
TvT: 5-(25,9,180) $\cup$ 5-(25,10,576)

4438 5-(28,8,756) (complement has $\lambda=1015$)
$A_8^{[2]}$ (>=1 isom. types)
derived from number 7410

7315 5-(29,9,756) (complement has $\lambda=9870$)
design of number 7314 with respect to smaller t

7410 6-(29,9,756) (complement has $\lambda=1015$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

5242 5-(33,8,756) (complement has $\lambda=2520$)
TvT: 5-(32,7,81) $\cup$ 5-(32,8,675)

3676 5-(24,9,764) (complement has $\lambda=3112$)
$PSL(2,23)$

6303 5-(25,9,765) (complement has $\lambda=4080$)
residual design of number 6301
derived from number 8047

8047 6-(26,10,765) (complement has $\lambda=4080$)
derived from number 8045

8045 7-(27,11,765) (complement has $\lambda=4080$)
$ASL(3,3)$ 189 isomorphism types

9593 5-(32,8,765) (complement has $\lambda=2160$)
derived from number 9589
design of number 9590 with respect to smaller t

9589 6-(33,9,765) (complement has $\lambda=2160$)
design of number 9588 with respect to smaller t

1392 5-(19,10,770) (complement has $\lambda=1232$)
TvT: 5-(18,9,275) $\cup$ 5-(18,10,495) \cite{TranvanTrung86}
supplementary design of number 1603

2100 5-(22,10,770) (complement has $\lambda=5418$)
$PGL(2,19)++$

7327 5-(28,9,770) (complement has $\lambda=8085$)
residual design of number 7324

2626 5-(24,10,774) (complement has $\lambda=10854$)
$PSL(2,23)$ (1163 isomorphism types) \cite{KitazumeMunemasa97}

1761 5-(20,10,777) (complement has $\lambda=2226$)
\cite{Krameretal85}
Alltop construction for design number 1763
\cite{Krameretal85} $PSL(2,19)$

3683 5-(24,9,780) (complement has $\lambda=3096$)
$PSL(2,23)$

1395 5-(19,10,784) (complement has $\lambda=1218$)
TvT: 5-(18,9,280) $\cup$ 5-(18,10,504) \cite{TranvanTrung86}
supplementary design of number 1607

2019 5-(22,11,784) (complement has $\lambda=11592$)
Alltop construction for design number 2016

7185 5-(28,8,784) (complement has $\lambda=987$)
residual design of number 7182
derived from number 7411

7411 6-(29,9,784) (complement has $\lambda=987$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}
residual design of number 9279

4442 5-(28,8,791) (complement has $\lambda=980$)
$S_8^{[2]}$ (>=1 isom. types)

2629 5-(24,10,792) (complement has $\lambda=10836$)
$PGL(2,23)$ (1 isomorphism type) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (1052 isomorphism types) \cite{KitazumeMunemasa97}

7301 5-(29,8,792) (complement has $\lambda=1232$)
design of number 7300 with respect to smaller t
residual design of number 7551
derived from number 7567

7567 6-(30,9,792) (complement has $\lambda=1232$)
(Tran van Trung construction): 6-(29,8,99) together with 6-(29,9,693) \cite{Bettenetal97b}

1398 5-(19,10,798) (complement has $\lambda=1204$)
TvT: 5-(18,9,285) $\cup$ 5-(18,10,513) \cite{TranvanTrung86}
supplementary design of number 1611

1545 5-(20,10,798) (complement has $\lambda=2205$)
Tran van Trung construction with supplementary design for design number 1543
Alltop construction for design number 1544
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

2107 5-(22,10,798) (complement has $\lambda=5390$)
$PGL(2,19)++$

7416 5-(28,8,798) (complement has $\lambda=973$)
derived from number 7414

7414 6-(29,9,798) (complement has $\lambda=973$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

9325 5-(29,8,800) (complement has $\lambda=1224$)
derived from number 9320
design of number 10647 with respect to smaller t

9320 6-(30,9,800) (complement has $\lambda=1224$)
derived from number 9318
design of number 10645 with respect to smaller t

9440 5-(31,8,800) (complement has $\lambda=1800$)
residual design of number 9434
derived from number 9435

9318 7-(31,10,800) (complement has $\lambda=1224$)
$PSL(3,5)$ ( >=1 isom. types)
design of number 10644 with respect to smaller t

9435 6-(32,9,800) (complement has $\lambda=1800$)
residual design of number 9432

5387 5-(46,8,800) (complement has $\lambda=9860$)
$M_{23}\times Id_2$ 2 solutions

4446 5-(28,8,805) (complement has $\lambda=966$)
Bluskov
design of number 7039 with respect to smaller t

10826 5-(23,9,810) (complement has $\lambda=2250$)
TvT: 5-(22,8,180) $\cup$ 5-(22,9,630)

3687 5-(24,9,810) (complement has $\lambda=3066$)
$PSL(2,23)$

2633 5-(24,10,810) (complement has $\lambda=10818$)
$PSL(2,23)$ (356 isomorphism types) \cite{KitazumeMunemasa97}

8063 5-(25,9,810) (complement has $\lambda=4035$)
derived from number 8059

8059 6-(26,10,810) (complement has $\lambda=4035$)
derived from number 8057

8057 7-(27,11,810) (complement has $\lambda=4035$)
$ASL(3,3)$ 1188 isomorphism types

5541 5-(19,10,812) (complement has $\lambda=1190$)
residual design of number 5539
supplementary design of number 5540
design of number 7812 with respect to smaller t

2114 5-(22,10,812) (complement has $\lambda=5376$)
$PGL(2,19)++$

1549 5-(20,10,819) (complement has $\lambda=2184$)
Tran van Trung construction with supplementary design for design number 1547
Alltop construction for design number 1548
\cite{Krameretal85}
\cite{TranvanTrung86}

3917 5-(26,10,819) (complement has $\lambda=19530$)
TvT: 5-(25,9,195) $\cup$ 5-(25,10,624)

7426 5-(28,8,819) (complement has $\lambda=952$)
derived from number 7424

7424 6-(29,9,819) (complement has $\lambda=952$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

1616 5-(19,10,826) (complement has $\lambda=1176$)
supplementary design of number 1615

7432 5-(28,8,826) (complement has $\lambda=945$)
derived from number 7430

7430 6-(29,9,826) (complement has $\lambda=945$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

2637 5-(24,10,828) (complement has $\lambda=10800$)
$PSL(2,23)$ (416 isomorphism types) \cite{KitazumeMunemasa97}

1554 5-(20,10,840) (complement has $\lambda=2163$)
Tran van Trung construction with supplementary design for design number 1551
Alltop construction for design number 1553
\cite{Krameretal85}
\cite{Krameretal85} $PSL(2,19)$

1897 5-(21,9,840) (complement has $\lambda=980$)
TvT: 5-(20,8,210) $\cup$ 5-(20,9,630)
derived from number 5569

1840 5-(21,10,840) (complement has $\lambda=3528$)
$PGL(2,19)+$
residual design of number 5563
derived from number 5570

1984 5-(22,9,840) (complement has $\lambda=1540$)
$PSL(2,19)++$
residual design of number 7831
derived from number 7832

2121 5-(22,10,840) (complement has $\lambda=5348$)
$PGL(2,19)++$

2026 5-(22,11,840) (complement has $\lambda=11536$)
Alltop construction for design number 2023
$PGL(2,19)++$

5569 6-(22,10,840) (complement has $\lambda=980$)
$PSL(2,19)++$

5570 6-(22,11,840) (complement has $\lambda=3528$)
$PGL(2,19)++$

7832 6-(23,10,840) (complement has $\lambda=1540$)
residual design of number 7829

3693 5-(24,9,840) (complement has $\lambda=3036$)
$PSL(2,23)$

8080 5-(25,9,840) (complement has $\lambda=4005$)
derived from number 8075

3789 5-(25,10,840) (complement has $\lambda=14664$)
TvT: 5-(24,9,210) $\cup$ 5-(24,10,630)

8075 6-(26,10,840) (complement has $\lambda=4005$)
derived from number 8073

8073 7-(27,11,840) (complement has $\lambda=4005$)
$ASL(3,3)$

4450 5-(28,8,840) (complement has $\lambda=931$)
$S_8^{[2]}$ (>=1 isom. types)
residual design of number 7191
derived from number 7440

7164 5-(29,8,840) (complement has $\lambda=1184$)
design of number 7163 with respect to smaller t
derived from number 7569

7440 6-(29,9,840) (complement has $\lambda=931$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

7569 6-(30,9,840) (complement has $\lambda=1184$)
(Tran van Trung construction): 6-(29,8,105) together with 6-(29,9,735) \cite{Bettenetal97b}
design of number 9278 with respect to smaller t

9386 5-(31,8,840) (complement has $\lambda=1760$)
derived from number 9382
residual design of number 9454

9382 6-(32,9,840) (complement has $\lambda=1760$)
derived from number 9380
residual design of number 9452

9380 7-(33,10,840) (complement has $\lambda=1760$)
$P\Gamma L(2,32)$ (many isomorphism types)

2641 5-(24,10,846) (complement has $\lambda=10782$)
$PSL(2,23)$ (139 isomorphism types) \cite{KitazumeMunemasa97}

7173 5-(29,8,848) (complement has $\lambda=1176$)
design of number 7172 with respect to smaller t

1623 5-(19,10,854) (complement has $\lambda=1148$)
supplementary design of number 1622

1560 5-(20,10,861) (complement has $\lambda=2142$)
Tran van Trung construction with supplementary design for design number 1558
Alltop construction for design number 1559
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

7448 5-(28,8,861) (complement has $\lambda=910$)
derived from number 7446

7446 6-(29,9,861) (complement has $\lambda=910$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

2645 5-(24,10,864) (complement has $\lambda=10764$)
$PSL(2,23)$ (117 isomorphism types) \cite{KitazumeMunemasa97}

5546 5-(19,10,868) (complement has $\lambda=1134$)
residual design of number 5544
supplementary design of number 5545
design of number 7819 with respect to smaller t

3697 5-(24,9,870) (complement has $\lambda=3006$)
$PSL(2,23)$

4454 5-(28,8,875) (complement has $\lambda=896$)
$S_8^{[2]}$ (>=1 isom. types)

3701 5-(24,9,876) (complement has $\lambda=3000$)
$PSL(2,23)$

9403 5-(31,8,880) (complement has $\lambda=1720$)
derived from number 9398

9398 6-(32,9,880) (complement has $\lambda=1720$)
derived from number 9396

9396 7-(33,10,880) (complement has $\lambda=1720$)
$P\Gamma L(2,32)$ (many isomorphism types)

1401 5-(19,10,882) (complement has $\lambda=1120$)
TvT: 5-(18,9,315) $\cup$ 5-(18,10,567) \cite{TranvanTrung86}
supplementary design of number 1629
design of number 5528 with respect to smaller t
residual design of number 5529

1565 5-(20,10,882) (complement has $\lambda=2121$)
Tran van Trung construction with supplementary design for design number 1562
Alltop construction for design number 1564
\cite{Krameretal85} $PGL(2,19)$

2124 5-(22,10,882) (complement has $\lambda=5306$)
$PGL(2,19)++$

2649 5-(24,10,882) (complement has $\lambda=10746$)
$PSL(2,23)$ (45 isomorphism types) \cite{KitazumeMunemasa97}

7199 5-(28,8,882) (complement has $\lambda=889$)
residual design of number 7197
derived from number 7452

7452 6-(29,9,882) (complement has $\lambda=889$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

5129 5-(32,8,885) (complement has $\lambda=2040$)
$AGL(4,2)\times C_2$

1404 5-(19,10,896) (complement has $\lambda=1106$)
TvT: 5-(18,9,320) $\cup$ 5-(18,10,576) \cite{TranvanTrung86}
supplementary design of number 1633

2131 5-(22,10,896) (complement has $\lambda=5292$)
$PGL(2,19)++$

7183 5-(29,8,896) (complement has $\lambda=1128$)
design of number 7182 with respect to smaller t
derived from number 7572

7572 6-(30,9,896) (complement has $\lambda=1128$)
(Tran van Trung construction): 6-(29,8,112) together with 6-(29,9,784) \cite{Bettenetal97b}
design of number 9279 with respect to smaller t

5245 5-(33,8,896) (complement has $\lambda=2380$)
\cite{Sebille98} $P\Gamma L(2,32)$

7883 5-(23,9,900) (complement has $\lambda=2160$)
residual design of number 7881
design of number 7882 with respect to smaller t

2653 5-(24,10,900) (complement has $\lambda=10728$)
$PSL(2,23)$ (14 isomorphism types) \cite{KitazumeMunemasa97}

8099 5-(25,9,900) (complement has $\lambda=3945$)
derived from number 8094

8094 6-(26,10,900) (complement has $\lambda=3945$)
derived from number 8092

8092 7-(27,11,900) (complement has $\lambda=3945$)
$ASL(3,3)$

4882 5-(30,8,900) (complement has $\lambda=1400$)
TvT: 5-(29,7,108) $\cup$ 5-(29,8,792)
design of number 7551 with respect to smaller t
derived from number 7651

7651 6-(31,9,900) (complement has $\lambda=1400$)
TvT: 6-(30,8,108) $\cup$ 6-(30,9,792)

9437 5-(32,8,900) (complement has $\lambda=2025$)
derived from number 9433
design of number 9434 with respect to smaller t

9433 6-(33,9,900) (complement has $\lambda=2025$)
design of number 9432 with respect to smaller t

5391 5-(46,8,900) (complement has $\lambda=9760$)
$M_{23}\times Id_2$ 2 solutions

1765 5-(20,10,903) (complement has $\lambda=2100$)
\cite{Krameretal85} $PSL(2,19)$
Alltop construction for design number 1767

1407 5-(19,10,910) (complement has $\lambda=1092$)
TvT: 5-(18,9,325) $\cup$ 5-(18,10,585) \cite{TranvanTrung86}
supplementary design of number 1637

1881 5-(21,9,910) (selfcomplementary)
$LS[2](5,9,21)$ $PSL(2,9)$
$P\GammaL(2,9)xid_2+$ Halving of the complete design
residual design of number 5561
residual design of complement of number 5561

1987 5-(22,9,910) (complement has $\lambda=1470$)
$PSL(2,19)++$

6995 5-(27,9,910) (complement has $\lambda=6405$)
derived from number 6993

6993 6-(28,10,910) (complement has $\lambda=6405$)
$P\Gamma L(2,27)$

2657 5-(24,10,918) (complement has $\lambda=10710$)
$PSL(2,23)$ (4 isomorphism types) \cite{KitazumeMunemasa97}

1642 5-(19,10,924) (complement has $\lambda=1078$)
supplementary design of number 1641

1769 5-(20,10,924) (complement has $\lambda=2079$)
\cite{Krameretal85}
Alltop construction for design number 1771
Tran van Trung construction with supplementary design for design number 5535

2033 5-(22,11,924) (complement has $\lambda=11452$)
Alltop construction for design number 2030

10829 5-(23,11,924) (complement has $\lambda=17640$)
TvT: 5-(22,10,308) $\cup$ 5-(22,11,616)

3708 5-(24,9,924) (complement has $\lambda=2952$)
$PGL(2,23)$ (>1 isomorphism types)

7325 5-(29,9,924) (complement has $\lambda=9702$)
design of number 7324 with respect to smaller t

8119 5-(25,9,930) (complement has $\lambda=3915$)
derived from number 8114

8114 6-(26,10,930) (complement has $\lambda=3915$)
derived from number 8112

8112 7-(27,11,930) (complement has $\lambda=3915$)
$ASL(3,3)$

2661 5-(24,10,936) (complement has $\lambda=10692$)
$PSL(2,23)$ (4 isomorphism types) \cite{KitazumeMunemasa97}
$PSL(2,23)$ (4 isomorphism types) \cite{KitazumeMunemasa97}

5550 5-(19,10,938) (complement has $\lambda=1064$)
residual design of number 5548
supplementary design of number 5549
design of number 7824 with respect to smaller t

2138 5-(22,10,938) (complement has $\lambda=5250$)
$PGL(2,19)++$

1572 5-(20,10,945) (complement has $\lambda=2058$)
Tran van Trung construction with supplementary design for design number 1569
Alltop construction for design number 1571
\cite{Krameretal85}
\cite{Krameretal85} $PGL(2,19)$

8138 5-(25,9,945) (complement has $\lambda=3900$)
derived from number 8133

245 5-(26,9,945) (complement has $\lambda=5040$)
derived from number 243
$PGL(2,25)$
design of number 6301 with respect to smaller t

3919 5-(26,10,945) (complement has $\lambda=19404$)
TvT: 5-(25,9,225) $\cup$ 5-(25,10,720)

8133 6-(26,10,945) (complement has $\lambda=3900$)
derived from number 8131

243 6-(27,10,945) (complement has $\lambda=5040$)
$ASL(3,3)^{13}$
TvT: 6-(26,9,180) $\cup$ 6-(26,10,765)

8131 7-(27,11,945) (complement has $\lambda=3900$)
$ASL(3,3)$

9455 5-(32,8,945) (complement has $\lambda=1980$)
derived from number 9453
design of number 9454 with respect to smaller t

9453 6-(33,9,945) (complement has $\lambda=1980$)
design of number 9452 with respect to smaller t
derived from number 9608

9608 7-(34,10,945) (complement has $\lambda=1980$)
TvT: 7-(33,9,105) $\cup$ 7-(33,10,840)

1649 5-(19,10,952) (complement has $\lambda=1050$)
supplementary design of number 1648

2145 5-(22,10,952) (complement has $\lambda=5236$)
\cite{Kreher95}
TvT: 5-(21,9,280) $\cup$ 5-(21,10,672)

1829 5-(22,11,952) (complement has $\lambda=11424$)
Tran van Trung construction with supplementary design for design number 1826
Alltop construction for design number 1828
$PSL(3,4)+$ 9 isomorphism types
$PGL(2,19)++$ 439 solutions
\cite{Kreher95}

833 5-(25,10,960) (complement has $\lambda=14544$)
TvT: 5-(24,9,240) $\cup$ 5-(24,10,720)

3840 5-(25,12,960) (complement has $\lambda=76560$)
TvT: 5-(24,11,336) $\cup$ 5-(24,12,624)

7192 5-(29,8,960) (complement has $\lambda=1064$)
design of number 7191 with respect to smaller t
derived from number 7575

7575 6-(30,9,960) (complement has $\lambda=1064$)
(Tran van Trung construction): 6-(29,8,120) together with 6-(29,9,840) \cite{Bettenetal97b}

9467 5-(31,8,960) (complement has $\lambda=1640$)
residual design of number 9461
derived from number 9462

9462 6-(32,9,960) (complement has $\lambda=1640$)
residual design of number 9459

5395 5-(46,8,960) (complement has $\lambda=9700$)
$M_{23}\times Id_2$

1578 5-(20,10,966) (complement has $\lambda=2037$)
Tran van Trung construction with supplementary design for design number 1576
Alltop construction for design number 1577
\cite{Krameretal85}
TvT: 5-(19,9,322) $\cup$ 5-(19,10,644) \cite{TranvanTrung86}
\cite{Krameretal85} $PSL(2,19)$
\cite{TranvanTrung86}

2147 5-(22,10,966) (complement has $\lambda=5222$)
$PGL(2,19)++$

1410 5-(19,10,980) (complement has $\lambda=1022$)
TvT: 5-(18,9,350) $\cup$ 5-(18,10,630) \cite{TranvanTrung86}
supplementary design of number 1662

2154 5-(22,10,980) (complement has $\lambda=5208$)
$PGL(2,19)++$

1582 5-(20,10,987) (complement has $\lambda=2016$)
Tran van Trung construction with supplementary design for design number 1580
Alltop construction for design number 1581
\cite{Krameretal85}
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

1413 5-(19,10,994) (complement has $\lambda=1008$)
TvT: 5-(18,9,355) $\cup$ 5-(18,10,639) \cite{TranvanTrung86}
supplementary design of number 1666

3714 5-(24,9,996) (complement has $\lambda=2880$)
$PGL(2,23)$ (>1 isomorphism types)

9424 5-(31,8,1000) (complement has $\lambda=1600$)
residual design of number 9419
derived from number 9481

9481 6-(32,9,1000) (complement has $\lambda=1600$)
residual design of number 9479

1586 5-(20,10,1008) (complement has $\lambda=1995$)
Tran van Trung construction with supplementary design for design number 1584
Alltop construction for design number 1585
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

1849 5-(21,10,1008) (complement has $\lambda=3360$)
$PGL(2,19)+$
derived from number 5571
design of number 5576 with respect to smaller t

2161 5-(22,10,1008) (complement has $\lambda=5180$)
$PGL(2,19)++$

2277 5-(22,11,1008) (complement has $\lambda=11368$)
\cite{Kreher95} $PSL(3,4)+$ 6 isomorphism types
Alltop construction for design number 2279

5571 6-(22,11,1008) (complement has $\lambda=3360$)
$PGL(2,19)++$
design of number 5575 with respect to smaller t
Tran van Trung construction with supplementary design for design number 5576

11019 5-(23,10,1008) (complement has $\lambda=7560$)
TvT: 5-(22,9,280) $\cup$ 5-(22,10,728)

3227 5-(24,9,1008) (complement has $\lambda=2868$)
$PGL(2,23)$ (>1 isomorphism types)

2397 5-(24,10,1008) (complement has $\lambda=10620$)
\cite{Driessen78}

3718 5-(25,10,1008) (complement has $\lambda=14496$)
TvT: 5-(24,9,252) $\cup$ 5-(24,10,756)

7198 5-(29,8,1008) (complement has $\lambda=1016$)
design of number 7197 with respect to smaller t
derived from number 7552

7552 6-(30,9,1008) (complement has $\lambda=1016$)
(Tran van Trung construction): 6-(29,8,126) together with 6-(29,9,882) \cite{Bettenetal97b}

10332 5-(38,8,1008) (complement has $\lambda=4448$)
derived from number 10327

10327 6-(39,9,1008) (complement has $\lambda=4448$)
derived from number 10325

10325 7-(40,10,1008) (complement has $\lambda=4448$)
$PSL(4,3)$ (many isomorphism types)

6307 5-(25,9,1020) (complement has $\lambda=3825$)
residual design of number 6306
derived from number 8011

8011 6-(26,10,1020) (complement has $\lambda=3825$)
residual design of number 8009

2168 5-(22,10,1022) (complement has $\lambda=5166$)
$PGL(2,19)++$

10994 5-(24,9,1026) (complement has $\lambda=2850$)
TvT: 5-(23,8,216) $\cup$ 5-(23,9,810)

10889 5-(24,10,1026) (complement has $\lambda=10602$)
TvT: 5-(23,9,270) $\cup$ 5-(23,10,756)

1590 5-(20,10,1029) (complement has $\lambda=1974$)
Tran van Trung construction with supplementary design for design number 1588
Alltop construction for design number 1589
\cite{Krameretal85}
\cite{TranvanTrung86}

840 5-(25,10,1032) (complement has $\lambda=14472$)
TvT: 5-(24,9,258) $\cup$ 5-(24,10,774)

8158 5-(25,9,1035) (complement has $\lambda=3810$)
derived from number 8153

8153 6-(26,10,1035) (complement has $\lambda=3810$)
derived from number 8151

8151 7-(27,11,1035) (complement has $\lambda=3810$)
$ASL(3,3)$

2042 5-(22,11,1036) (complement has $\lambda=11340$)
Alltop construction for design number 2039

1677 5-(20,10,1050) (complement has $\lambda=1953$)
\cite{Krameretal85} $PGL(2,19)$
Alltop construction for design number 1679

1991 5-(22,9,1050) (complement has $\lambda=1330$)
$PSL(2,19)++$

2175 5-(22,10,1050) (complement has $\lambda=5138$)
$PGL(2,19)++$

3720 5-(25,10,1056) (complement has $\lambda=14448$)
TvT: 5-(24,9,264) $\cup$ 5-(24,10,792)

5351 5-(46,8,1060) (complement has $\lambda=9600$)
$M_{23}\times Id_2$

3234 5-(24,9,1068) (complement has $\lambda=2808$)
$PGL(2,23)$ (>1 isomorphism types)

1681 5-(20,10,1071) (complement has $\lambda=1932$)
\cite{Krameretal85} $PGL(2,19)$
Alltop construction for design number 1683

7834 5-(23,9,1080) (complement has $\lambda=1980$)
derived from number 7830
design of number 7831 with respect to smaller t
residual design of number 7885

3240 5-(24,9,1080) (complement has $\lambda=2796$)
$M_{11}_{12}\times id_2$ 9 solutions
$PGL(2,23)$ (>1 isomorphism types)

7830 6-(24,10,1080) (complement has $\lambda=1980$)
design of number 7829 with respect to smaller t
residual design of number 7888

8174 5-(25,9,1080) (complement has $\lambda=3765$)
derived from number 8172

8172 6-(26,10,1080) (complement has $\lambda=3765$)
derived from number 8171

8171 7-(27,11,1080) (complement has $\lambda=3765$)
$ASL(3,3)$

9464 5-(32,8,1080) (complement has $\lambda=1845$)
derived from number 9460
design of number 9461 with respect to smaller t

9460 6-(33,9,1080) (complement has $\lambda=1845$)
design of number 9459 with respect to smaller t

7693 5-(36,8,1080) (complement has $\lambda=3415$)
derived from number 7691

7691 6-(37,9,1080) (complement has $\lambda=3415$)
$Sp(6,2)_36+$ (many isom. types)

5133 5-(32,8,1085) (complement has $\lambda=1840$)
$AGL(4,2)\times C_2$

3244 5-(24,9,1086) (complement has $\lambda=2790$)
$PSL(2,23)$ (>1 isomorphism types)

1595 5-(20,10,1092) (complement has $\lambda=1911$)
Tran van Trung construction with supplementary design for design number 1592
Alltop construction for design number 1594
\cite{Krameretal85} $PSL(2,19)$

2048 5-(22,11,1092) (complement has $\lambda=11284$)
Alltop construction for design number 2045

4885 5-(30,9,1100) (complement has $\lambda=11550$)
TvT: 5-(29,8,176) $\cup$ 5-(29,9,924)

3248 5-(24,9,1104) (complement has $\lambda=2772$)
$PGL(2,23)$ (>1 isomorphism types)

8188 5-(25,9,1110) (complement has $\lambda=3735$)
derived from number 8183

8183 6-(26,10,1110) (complement has $\lambda=3735$)
derived from number 8181

8181 7-(27,11,1110) (complement has $\lambda=3735$)
$ASL(3,3)$

1685 5-(20,10,1113) (complement has $\lambda=1890$)
\cite{Krameretal85} $PGL(2,19)$
Alltop construction for design number 1687

3252 5-(24,9,1116) (complement has $\lambda=2760$)
$PGL(2,23)$ (>1 isomorphism types)

1995 5-(22,9,1120) (complement has $\lambda=1260$)
$PSL(2,19)++$
residual design of number 7839
derived from number 7840

2055 5-(22,11,1120) (complement has $\lambda=11256$)
Alltop construction for design number 2052
\cite{Kreher95} $PSL(3,4)+$ 9 isomorphism types $PGL(2,19)++$

7840 6-(23,10,1120) (complement has $\lambda=1260$)
residual design of number 7837

9497 5-(31,8,1120) (complement has $\lambda=1480$)
residual design of number 9491
derived from number 9492

5137 5-(32,8,1120) (complement has $\lambda=1805$)
$AGL(4,2)\times C_2$

9492 6-(32,9,1120) (complement has $\lambda=1480$)
residual design of number 9489

5355 5-(46,8,1120) (complement has $\lambda=9540$)
$M_{23}\times Id_2$

3256 5-(24,9,1122) (complement has $\lambda=2754$)
$PSL(2,23)$ (>1 isomorphism types)

5141 5-(32,8,1125) (complement has $\lambda=1800$)
$AGL(4,2)\times C_2$
residual design of number 9417
design of number 9419 with respect to smaller t
derived from number 9480

9480 6-(33,9,1125) (complement has $\lambda=1800$)
design of number 9479 with respect to smaller t
residual design of number 9609

3260 5-(24,9,1128) (complement has $\lambda=2748$)
$PSL(2,23)$ (>1 isomorphism types)

3722 5-(25,10,1128) (complement has $\lambda=14376$)
TvT: 5-(24,9,282) $\cup$ 5-(24,10,846)

1601 5-(20,10,1134) (complement has $\lambda=1869$)
Tran van Trung construction with supplementary design for design number 1599
Alltop construction for design number 1600
\cite{Krameretal85}
\cite{TranvanTrung86}

10832 5-(23,11,1134) (complement has $\lambda=17430$)
TvT: 5-(22,10,378) $\cup$ 5-(22,11,756)

3267 5-(24,9,1140) (complement has $\lambda=2736$)
$PGL(2,23)$ (>1 isomorphism types)
residual design of number 6275
design of number 7881 with respect to smaller t

3271 5-(24,9,1152) (complement has $\lambda=2724$)
$PGL(2,23)$ (>1 isomorphism types)

1605 5-(20,10,1155) (complement has $\lambda=1848$)
Tran van Trung construction with supplementary design for design number 1603
Alltop construction for design number 1604
\cite{Krameretal85} $PSL(2,19)$
\cite{TranvanTrung86}

5578 5-(20,11,1155) (complement has $\lambda=3850$)
residual design of number 5577

4133 5-(27,9,1155) (complement has $\lambda=6160$)
TvT: 5-(26,8,210) $\cup$ 5-(26,9,945)

3274 5-(24,9,1158) (complement has $\lambda=2718$)
$PGL(2,23)$ (>1 isomorphism types)

9517 5-(31,8,1160) (complement has $\lambda=1440$)
residual design of number 9511
derived from number 9512

9512 6-(32,9,1160) (complement has $\lambda=1440$)
residual design of number 9509

3278 5-(24,9,1170) (complement has $\lambda=2706$)
$PGL(2,23)$ (>1 isomorphism types)

8208 5-(25,9,1170) (complement has $\lambda=3675$)
derived from number 8203

8203 6-(26,10,1170) (complement has $\lambda=3675$)
derived from number 8201

8201 7-(27,11,1170) (complement has $\lambda=3675$)
$ASL(3,3)$

1609 5-(20,10,1176) (complement has $\lambda=1827$)
Tran van Trung construction with supplementary design for design number 1607
Alltop construction for design number 1608
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

2062 5-(22,11,1176) (complement has $\lambda=11200$)
Alltop construction for design number 2059

10960 5-(23,11,1176) (complement has $\lambda=17388$)
TvT: 5-(22,10,392) $\cup$ 5-(22,11,784)

3282 5-(24,9,1176) (complement has $\lambda=2700$)
$M_{11}_{12}\times id_2$
$PGL(2,23)$ (>1 isomorphism types)
derived from number 7907

7907 6-(25,10,1176) (complement has $\lambda=2700$)
derived from number 7905

7905 7-(26,11,1176) (complement has $\lambda=2700$)
$P\Gamma L(2,25)$(>=1 isom. type)

3286 5-(24,9,1188) (complement has $\lambda=2688$)
$PGL(2,23)$ (>1 isomorphism types)

5562 5-(22,9,1190) (selfcomplementary)
design of number 5561 with respect to smaller t
complementary design of number 5561 with respect to smaller t
derived from number 5585
derived from complement of number 5585
residual design of number 5660
residual design of complement of number 5660

5564 5-(22,10,1190) (complement has $\lambda=4998$)
design of number 5563 with respect to smaller t
derived from number 11494

5585 6-(23,10,1190) (selfcomplementary)
residual 7-(24,10,340) Halving of the complete design
residual design of number 7846
residual design of complement of number 7846

11494 6-(23,11,1190) (complement has $\lambda=4998$)
TvT: 6-(22,10,350) $\cup$ 6-(22,11,840)
derived from number 11497

11497 7-(24,12,1190) (complement has $\lambda=4998$)
Alltop construction for design number 11494

3290 5-(24,9,1194) (complement has $\lambda=2682$)
$PGL(2,23)$ (>1 isomorphism types)

1613 5-(20,10,1197) (complement has $\lambda=1806$)
Tran van Trung construction with supplementary design for design number 1611
Alltop construction for design number 1612
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

8226 5-(25,9,1200) (complement has $\lambda=3645$)
derived from number 8222

8222 6-(26,10,1200) (complement has $\lambda=3645$)
derived from number 8220

8220 7-(27,11,1200) (complement has $\lambda=3645$)
$ASL(3,3)$

2069 5-(22,11,1204) (complement has $\lambda=11172$)
Alltop construction for design number 2066

5145 5-(32,8,1205) (complement has $\lambda=1720$)
$AGL(4,2)\times C_2$

10352 5-(38,8,1208) (complement has $\lambda=4248$)
derived from number 10347

10347 6-(39,9,1208) (complement has $\lambda=4248$)
derived from number 10345

10345 7-(40,10,1208) (complement has $\lambda=4248$)
$PSL(4,3)$ (many isomorphism types)

8239 5-(25,9,1215) (complement has $\lambda=3630$)
derived from number 8237

8237 6-(26,10,1215) (complement has $\lambda=3630$)
derived from number 8236

8236 7-(27,11,1215) (complement has $\lambda=3630$)
\cite{Sebille98} $AGL(3,3)$

1689 5-(20,10,1218) (complement has $\lambda=1785$)
\cite{Krameretal85} $PSL(2,19)$
Alltop construction for design number 1691
design of number 5539 with respect to smaller t
Tran van Trung construction with supplementary design for design number 5540

5359 5-(46,8,1220) (complement has $\lambda=9440$)
$M_{23}\times Id_2$

3298 5-(24,9,1224) (complement has $\lambda=2652$)
$PGL(2,23)$ (>1 isomorphism types)
residual design of number 8002

3724 5-(25,10,1224) (complement has $\lambda=14280$)
TvT: 5-(24,9,306) $\cup$ 5-(24,10,918)

6834 5-(27,9,1225) (complement has $\lambda=6090$)
derived from number 6832

6832 6-(28,10,1225) (complement has $\lambda=6090$)
$P\Gamma L(2,27)$

1834 5-(21,11,1232) (complement has $\lambda=6776$)
supplementary design of number 1833

1618 5-(20,10,1239) (complement has $\lambda=1764$)
Tran van Trung construction with supplementary design for design number 1615
Alltop construction for design number 1617
\cite{Krameretal85}

844 5-(25,10,1248) (complement has $\lambda=14256$)
TvT: 5-(24,9,312) $\cup$ 5-(24,10,936)

1697 5-(20,10,1260) (complement has $\lambda=1743$)
\cite{Krameretal85} $PGL(2,19)$
Alltop construction for design number 1699

2182 5-(22,10,1260) (complement has $\lambda=4928$)
$PGL(2,19)++$

2076 5-(22,11,1260) (complement has $\lambda=11116$)
Alltop construction for design number 2073

10835 5-(23,11,1260) (complement has $\lambda=17304$)
TvT: 5-(22,10,420) $\cup$ 5-(22,11,840)

3305 5-(24,9,1260) (complement has $\lambda=2616$)
$PGL(2,23)$ (>1 isomorphism types)

3975 5-(26,9,1260) (complement has $\lambda=4725$)
$PGL(2,25)$
design of number 6306 with respect to smaller t
derived from number 8010

857 5-(26,10,1260) (complement has $\lambda=19089$)
TvT: 5-(25,9,300) $\cup$ 5-(25,10,960)

8010 6-(27,10,1260) (complement has $\lambda=4725$)
design of number 8009 with respect to smaller t

7333 5-(28,9,1260) (complement has $\lambda=7595$)
residual design of number 7331

9494 5-(32,8,1260) (complement has $\lambda=1665$)
derived from number 9490
design of number 9491 with respect to smaller t

9420 5-(33,8,1260) (complement has $\lambda=2016$)
design of number 9417 with respect to smaller t
derived from number 9610

9490 6-(33,9,1260) (complement has $\lambda=1665$)
design of number 9489 with respect to smaller t

9610 6-(34,9,1260) (complement has $\lambda=2016$)
design of number 9609 with respect to smaller t
derived from number 10667

10667 7-(35,10,1260) (complement has $\lambda=2016$)
derived from number 10666

10666 8-(36,11,1260) (complement has $\lambda=2016$)
$Sp(6,2)_36$ (many isomorphism types) Betten, Laue, Suleiman, Wassermann 1997

3309 5-(24,9,1266) (complement has $\lambda=2610$)
$M_{11}_{12}\times id_2$

9537 5-(31,8,1280) (complement has $\lambda=1320$)
residual design of number 9531
derived from number 9532

9532 6-(32,9,1280) (complement has $\lambda=1320$)
residual design of number 9529

5363 5-(46,8,1280) (complement has $\lambda=9380$)
$M_{23}\times Id_2$

1625 5-(20,10,1281) (complement has $\lambda=1722$)
Tran van Trung construction with supplementary design for design number 1622
Alltop construction for design number 1624
\cite{Krameretal85} $PSL(2,19)$

3313 5-(24,9,1284) (complement has $\lambda=2592$)
$PGL(2,23)$ (>1 isomorphism types)

2281 5-(22,11,1288) (complement has $\lambda=11088$)
\cite{Kreher95} $PSL(3,4)+$ 6 isomorphism types
Alltop construction for design number 2283

3317 5-(24,9,1296) (complement has $\lambda=2580$)
$M_{11}_{12}\times id_2$
$PGL(2,23)$ (>1 isomorphism types)
residual design of number 6278
derived from number 10501

10501 6-(25,10,1296) (complement has $\lambda=2580$)
derived from number 10499

10499 7-(26,11,1296) (complement has $\lambda=2580$)
derived from number 10498

10498 8-(27,12,1296) (complement has $\lambda=2580$)
$ASL(3,3)$ 8672 solutions 4336 isomorphism types

10372 5-(38,8,1296) (complement has $\lambda=4160$)
derived from number 10367

10367 6-(39,9,1296) (complement has $\lambda=4160$)
derived from number 10365

10365 7-(40,10,1296) (complement has $\lambda=4160$)
$PSL(4,3)$ (many isomorphism types)

5013 5-(31,9,1300) (complement has $\lambda=13650$)
TvT: 5-(30,8,200) $\cup$ 5-(30,9,1100)

5149 5-(32,8,1300) (complement has $\lambda=1625$)
$AGL(4,2)\times C_2$

1701 5-(20,10,1302) (complement has $\lambda=1701$)
\cite{Krameretal85} $PGL(2,19)$
Alltop construction for design number 1703
\cite{TranvanTrung86}
design of number 5544 with respect to smaller t
Tran van Trung construction with supplementary design for design number 5545

2189 5-(22,10,1302) (complement has $\lambda=4886$)
$PGL(2,19)++$

3321 5-(24,9,1302) (complement has $\lambda=2574$)
$PGL(2,23)$ (>1 isomorphism types)

8249 5-(25,9,1305) (complement has $\lambda=3540$)
derived from number 8247

8247 6-(26,10,1305) (complement has $\lambda=3540$)
derived from number 8246

8246 7-(27,11,1305) (complement has $\lambda=3540$)
\cite{Sebille98} $AGL(3,3)$

9514 5-(32,8,1305) (complement has $\lambda=1620$)
derived from number 9510
design of number 9511 with respect to smaller t

9510 6-(33,9,1305) (complement has $\lambda=1620$)
design of number 9509 with respect to smaller t

3328 5-(24,9,1320) (complement has $\lambda=2556$)
$PGL(2,23)$ (>1 isomorphism types)

1631 5-(20,10,1323) (complement has $\lambda=1680$)
Tran van Trung construction with supplementary design for design number 1629
Alltop construction for design number 1630
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}
design of number 5529 with respect to smaller t

3899 5-(26,10,1323) (complement has $\lambda=19026$)
TvT: 5-(25,9,315) $\cup$ 5-(25,10,1008)

3332 5-(24,9,1332) (complement has $\lambda=2544$)
$PGL(2,23)$ (>1 isomorphism types)

8263 5-(25,9,1335) (complement has $\lambda=3510$)
derived from number 8258

8258 6-(26,10,1335) (complement has $\lambda=3510$)
derived from number 8256

8256 7-(27,11,1335) (complement has $\lambda=3510$)
$ASL(3,3)$

1635 5-(20,10,1344) (complement has $\lambda=1659$)
Tran van Trung construction with supplementary design for design number 1633
Alltop construction for design number 1634
\cite{TranvanTrung86}

1802 5-(21,10,1344) (complement has $\lambda=3024$)
TvT: 5-(20,9,420) $\cup$ 5-(20,10,924)

2083 5-(22,11,1344) (complement has $\lambda=11032$)
Alltop construction for design number 2080
$PSL(3,4)+$ 9 isomorphism types

3336 5-(24,9,1350) (complement has $\lambda=2526$)
$PGL(2,23)$ (>1 isomorphism types)

8278 5-(25,9,1350) (complement has $\lambda=3495$)
derived from number 8276

8276 6-(26,10,1350) (complement has $\lambda=3495$)
derived from number 8275

8275 7-(27,11,1350) (complement has $\lambda=3495$)
\cite{Sebille98} $AGL(3,3)$

3340 5-(24,9,1356) (complement has $\lambda=2520$)
$PGL(2,23)$ (>1 isomorphism types)
derived from number 7920

7920 6-(25,10,1356) (complement has $\lambda=2520$)
derived from number 7918

7918 7-(26,11,1356) (complement has $\lambda=2520$)
$P\Gamma L(2,25)$(>=1 isom. type)

1639 5-(20,10,1365) (complement has $\lambda=1638$)
Tran van Trung construction with supplementary design for design number 1637
Alltop construction for design number 1638
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

3344 5-(24,9,1368) (complement has $\lambda=2508$)
$PGL(2,23)$ (>1 isomorphism types)
design of number 7885 with respect to smaller t
derived from number 7889
residual design of number 7896

11032 5-(24,10,1368) (complement has $\lambda=10260$)
TvT: 5-(23,9,360) $\cup$ 5-(23,10,1008)

10893 5-(25,10,1368) (complement has $\lambda=14136$)
TvT: 5-(24,9,342) $\cup$ 5-(24,10,1026)

7889 6-(25,10,1368) (complement has $\lambda=2508$)
design of number 7888 with respect to smaller t
residual design of number 7901

2090 5-(22,11,1372) (complement has $\lambda=11004$)
Alltop construction for design number 2087

3348 5-(24,9,1374) (complement has $\lambda=2502$)
$PGL(2,23)$ (>1 isomorphism types)

8291 5-(25,9,1380) (complement has $\lambda=3465$)
derived from number 8286

8286 6-(26,10,1380) (complement has $\lambda=3465$)
derived from number 8284

8284 7-(27,11,1380) (complement has $\lambda=3465$)
$ASL(3,3)$

5367 5-(46,8,1380) (complement has $\lambda=9280$)
$M_{23}\times Id_2$

1644 5-(20,10,1386) (complement has $\lambda=1617$)
Tran van Trung construction with supplementary design for design number 1641
Alltop construction for design number 1643
\cite{Krameretal85} $PGL(2,19)$
residual design of number 5581
derived from number 5582

5582 6-(21,11,1386) (complement has $\lambda=1617$)
residual design of number 5580
supplementary design of number 5581

2196 5-(22,10,1386) (complement has $\lambda=4802$)
$PGL(2,19)++$

11020 5-(23,11,1386) (complement has $\lambda=17178$)
TvT: 5-(22,10,462) $\cup$ 5-(22,11,924)

3355 5-(24,9,1386) (complement has $\lambda=2490$)
$PGL(2,23)$ (>1 isomorphism types)

3359 5-(24,9,1404) (complement has $\lambda=2472$)
$PGL(2,23)$ (>1 isomorphism types)

1705 5-(20,10,1407) (complement has $\lambda=1596$)
\cite{Krameretal85} $PSL(2,19)$
Alltop construction for design number 1707
design of number 5548 with respect to smaller t
Tran van Trung construction with supplementary design for design number 5549

3363 5-(24,9,1416) (complement has $\lambda=2460$)
$PGL(2,23)$ (>1 isomorphism types)

3367 5-(24,9,1422) (complement has $\lambda=2454$)
$PGL(2,23)$ (>1 isomorphism types)

6276 5-(25,9,1425) (complement has $\lambda=3420$)
design of number 6275 with respect to smaller t

9620 5-(32,8,1425) (complement has $\lambda=1500$)
residual design of number 9615
derived from number 9616

9616 6-(33,9,1425) (complement has $\lambda=1500$)
residual design of number 9613

1651 5-(20,10,1428) (complement has $\lambda=1575$)
Tran van Trung construction with supplementary design for design number 1648
Alltop construction for design number 1650
\cite{Krameretal85} $PGL(2,19)$

2203 5-(22,10,1428) (complement has $\lambda=4760$)
\cite{Kreher95} $PGL(2,19)++$
TvT: 5-(21,9,420) $\cup$ 5-(21,10,1008) \cite{TranvanTrung86}

2321 5-(23,11,1428) (complement has $\lambda=17136$)
TvT: 5-(22,10,476) $\cup$ 5-(22,11,952)

8005 5-(24,9,1428) (complement has $\lambda=2448$)
residual design of number 8004

3371 5-(24,9,1434) (complement has $\lambda=2442$)
$PGL(2,23)$ (>1 isomorphism types)

7842 5-(23,9,1440) (complement has $\lambda=1620$)
derived from number 7838
design of number 7839 with respect to smaller t
residual design of number 7887

7838 6-(24,10,1440) (complement has $\lambda=1620$)
design of number 7837 with respect to smaller t
residual design of number 7891

3873 5-(25,9,1440) (complement has $\lambda=3405$)
TvT: 5-(24,8,288) $\cup$ 5-(24,9,1152)
derived from number 8299

3935 5-(26,12,1440) (complement has $\lambda=114840$)
TvT: 5-(25,11,480) $\cup$ 5-(25,12,960)

8299 6-(26,10,1440) (complement has $\lambda=3405$)
derived from number 8298

8298 7-(27,11,1440) (complement has $\lambda=3405$)
\cite{Sebille98} $AGL(3,3)$

9534 5-(32,8,1440) (complement has $\lambda=1485$)
derived from number 9530
design of number 9531 with respect to smaller t

9530 6-(33,9,1440) (complement has $\lambda=1485$)
design of number 9529 with respect to smaller t

10691 5-(37,8,1440) (complement has $\lambda=3520$)
derived from number 10682

10682 6-(38,9,1440) (complement has $\lambda=3520$)
derived from number 10677

10677 7-(39,10,1440) (complement has $\lambda=3520$)
derived from number 10675

10675 8-(40,11,1440) (complement has $\lambda=3520$)
$PSL(4,3)$ (>= 89000 isomorphism types) Betten, Laue, Wassermann 1997

5371 5-(46,8,1440) (complement has $\lambda=9220$)
$M_{23}\times Id_2$

5153 5-(32,8,1445) (complement has $\lambda=1480$)
$AGL(4,2)\times C_2$

3377 5-(24,9,1446) (complement has $\lambda=2430$)
$PSL(2,23)$ (>1 isomorphism types)

1709 5-(20,10,1449) (complement has $\lambda=1554$)
\cite{Krameretal85}
Alltop construction for design number 1711

508 5-(22,11,1456) (complement has $\lambda=10920$)
Alltop construction for design number 505
PSL(3,4)+ Alltop construction from 4-(21,10,1456)
\cite{Kreher95} $PSL(3,4)+$ $PGL(2,19)++$

1664 5-(20,10,1470) (complement has $\lambda=1533$)
Tran van Trung construction with supplementary design for design number 1662
Alltop construction for design number 1663
\cite{Krameretal85} $PSL(2,19)$
\cite{TranvanTrung86}

8307 5-(25,9,1470) (complement has $\lambda=3375$)
derived from number 8306

8306 6-(26,10,1470) (complement has $\lambda=3375$)
derived from number 8305

8305 7-(27,11,1470) (complement has $\lambda=3375$)
\cite{Sebille98} $AGL(3,3)$

7339 5-(28,9,1470) (complement has $\lambda=7385$)
residual design of number 7337

3381 5-(24,9,1476) (complement has $\lambda=2400$)
$PGL(2,23)$ (>1 isomorphism types)

3385 5-(24,9,1482) (complement has $\lambda=2394$)
$PGL(2,23)$ (>1 isomorphism types)

8312 5-(25,9,1485) (complement has $\lambda=3360$)
derived from number 8310

8310 6-(26,10,1485) (complement has $\lambda=3360$)
derived from number 8309

8309 7-(27,11,1485) (complement has $\lambda=3360$)
\cite{Sebille98} $AGL(3,3)$

1668 5-(20,10,1491) (complement has $\lambda=1512$)
Tran van Trung construction with supplementary design for design number 1666
Alltop construction for design number 1667
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

3389 5-(24,9,1494) (complement has $\lambda=2382$)
$PGL(2,23)$ (>1 isomorphism types)

3396 5-(24,9,1500) (complement has $\lambda=2376$)
$M_{11}_{12}\times id_2$

3400 5-(24,9,1506) (complement has $\lambda=2370$)
$PSL(2,23)$ (>1 isomorphism types)

1852 5-(21,10,1512) (complement has $\lambda=2856$)
$PGL(2,19)+$
derived from number 5572

2205 5-(22,10,1512) (complement has $\lambda=4676$)
$PGL(2,19)++$

2099 5-(22,11,1512) (complement has $\lambda=10864$)
Alltop construction for design number 2096
\cite{Kreher95} $PSL(3,4)+$

5572 6-(22,11,1512) (complement has $\lambda=2856$)
$PGL(2,19)++$

7332 5-(29,9,1512) (complement has $\lambda=9114$)
design of number 7331 with respect to smaller t
derived from number 7458
residual design of number 7555

7458 6-(30,10,1512) (complement has $\lambda=9114$)
$P\Gamma L(2,27)++$ (>= 168 isom. types) \cite{Bettenetal97b}

8324 5-(25,9,1515) (complement has $\lambda=3330$)
derived from number 8319

8319 6-(26,10,1515) (complement has $\lambda=3330$)
derived from number 8317

8317 7-(27,11,1515) (complement has $\lambda=3330$)
$ASL(3,3)$

3404 5-(24,9,1518) (complement has $\lambda=2358$)
$PGL(2,23)$ (>1 isomorphism types)

3408 5-(24,9,1524) (complement has $\lambda=2352$)
$PGL(2,23)$ (>1 isomorphism types)

5661 5-(23,9,1530) (selfcomplementary)
design of number 5660 with respect to smaller t
complementary design of number 5660 with respect to smaller t
derived from number 5662
derived from complement of number 5662
residual design of number 5787
residual design of complement of number 5787

3412 5-(24,9,1530) (complement has $\lambda=2346$)
$PGL(2,23)$ (>1 isomorphism types)

5662 6-(24,10,1530) (selfcomplementary)
PSL(2,23) (>=1 isom. types) Halving of the complete design
design of number 7846 with respect to smaller t
complementary design of number 7846 with respect to smaller t

6311 5-(25,9,1530) (complement has $\lambda=3315$)
residual design of number 6309
design of number 8002 with respect to smaller t

7940 5-(24,9,1536) (complement has $\lambda=2340$)
derived from number 7936

7936 6-(25,10,1536) (complement has $\lambda=2340$)
derived from number 7934

7934 7-(26,11,1536) (complement has $\lambda=2340$)
$P\Gamma L(2,25)$(>=1 isom. type)

1841 5-(21,11,1540) (complement has $\lambda=6468$)
supplementary design of number 1840
residual design of number 5570

2106 5-(22,11,1540) (complement has $\lambda=10836$)
Alltop construction for design number 2103

4135 5-(27,9,1540) (complement has $\lambda=5775$)
TvT: 5-(26,8,280) $\cup$ 5-(26,9,1260)
derived from number 4189

4189 6-(28,10,1540) (complement has $\lambda=5775$)
\cite{Sebille98} $P\Gamma L(2,25)\cup S_2$
\cite{Sebille98} $P\Gamma L(2,25)\cup S_2$

7683 5-(35,8,1540) (complement has $\lambda=2520$)
derived from number 7681

7681 6-(36,9,1540) (complement has $\lambda=2520$)
$Sp(6,2)_36$ (many isom. types)

3416 5-(24,9,1548) (complement has $\lambda=2328$)
$PGL(2,23)$ (>1 isomorphism types)

10838 5-(23,11,1554) (complement has $\lambda=17010$)
TvT: 5-(22,10,518) $\cup$ 5-(22,11,1036)

3422 5-(24,9,1560) (complement has $\lambda=2316$)
$PGL(2,23)$ (>1 isomorphism types)

3841 5-(25,13,1560) (complement has $\lambda=124410$)
supplementary design of number 3840

3426 5-(24,9,1566) (complement has $\lambda=2310$)
$M_{11}_{12}\times id_2$

10392 5-(38,8,1568) (complement has $\lambda=3888$)
derived from number 10387

10387 6-(39,9,1568) (complement has $\lambda=3888$)
derived from number 10385

10385 7-(40,10,1568) (complement has $\lambda=3888$)
$PSL(4,3)$ (many isomorphism types)

8340 5-(25,9,1575) (complement has $\lambda=3270$)
derived from number 8338

8338 6-(26,10,1575) (complement has $\lambda=3270$)
derived from number 8337

8337 7-(27,11,1575) (complement has $\lambda=3270$)
\cite{Sebille98} $AGL(3,3)$

4458 5-(28,9,1575) (complement has $\lambda=7280$)
$Sp(6,2)$ (1 isom. type)

3430 5-(24,9,1578) (complement has $\lambda=2298$)
$PGL(2,23)$ (>1 isomorphism types)

10830 5-(23,12,1584) (complement has $\lambda=30240$)
supplementary design of number 10829

3434 5-(24,9,1584) (complement has $\lambda=2292$)
$PGL(2,23)$ (>1 isomorphism types)

2113 5-(22,11,1596) (complement has $\lambda=10780$)
Alltop construction for design number 2110

3438 5-(24,9,1596) (complement has $\lambda=2280$)
$PGL(2,23)$ (>1 isomorphism types)

5234 5-(33,8,1596) (complement has $\lambda=1680$)
$P\Gamma L(2,32)$
derived from number 9614
design of number 9615 with respect to smaller t

9614 6-(34,9,1596) (complement has $\lambda=1680$)
design of number 9613 with respect to smaller t

3442 5-(24,9,1602) (complement has $\lambda=2274$)
$PGL(2,23)$ (>1 isomorphism types)

8349 5-(25,9,1605) (complement has $\lambda=3240$)
derived from number 8347

8347 6-(26,10,1605) (complement has $\lambda=3240$)
derived from number 8346

8346 7-(27,11,1605) (complement has $\lambda=3240$)
\cite{Sebille98} $AGL(3,3)$

3446 5-(24,9,1608) (complement has $\lambda=2268$)
$PGL(2,23)$ (>1 isomorphism types)

7345 5-(28,9,1610) (complement has $\lambda=7245$)
residual design of number 7343

3450 5-(24,9,1614) (complement has $\lambda=2262$)
$PSL(2,23)$ (>1 isomorphism types)

3454 5-(24,9,1620) (complement has $\lambda=2256$)
$PGL(2,23)$ (>1 isomorphism types)

6279 5-(25,9,1620) (complement has $\lambda=3225$)
design of number 6278 with respect to smaller t
derived from number 8356

8356 6-(26,10,1620) (complement has $\lambda=3225$)
derived from number 8355

8355 7-(27,11,1620) (complement has $\lambda=3225$)
\cite{Sebille98} $AGL(3,3)$

2120 5-(22,11,1624) (complement has $\lambda=10752$)
Alltop construction for design number 2117

3458 5-(24,9,1632) (complement has $\lambda=2244$)
$PGL(2,23)$ (>1 isomorphism types)

10963 5-(23,11,1638) (complement has $\lambda=16926$)
TvT: 5-(22,10,546) $\cup$ 5-(22,11,1092)

3462 5-(24,9,1638) (complement has $\lambda=2238$)
$PGL(2,23)$ (>1 isomorphism types)

239 5-(27,9,1645) (complement has $\lambda=5670$)
$ASL(3,3)^{13}$

8369 5-(25,9,1650) (complement has $\lambda=3195$)
derived from number 8364

8364 6-(26,10,1650) (complement has $\lambda=3195$)
derived from number 8362

8362 7-(27,11,1650) (complement has $\lambda=3195$)
$ASL(3,3)$

7644 5-(30,9,1650) (complement has $\lambda=11000$)
residual design of number 7641

3466 5-(24,9,1656) (complement has $\lambda=2220$)
$PGL(2,23)$ (>1 isomorphism types)

10412 5-(38,8,1656) (complement has $\lambda=3800$)
derived from number 10407

10407 6-(39,9,1656) (complement has $\lambda=3800$)
derived from number 10405

10405 7-(40,10,1656) (complement has $\lambda=3800$)
$PSL(4,3)$ (many isomorphism types)

3470 5-(24,9,1674) (complement has $\lambda=2202$)
$PGL(2,23)$ (>1 isomorphism types)

2417 5-(24,10,1674) (complement has $\lambda=9954$)
$PSL(2,23)$

1809 5-(21,10,1680) (complement has $\lambda=2688$)
TvT: 5-(20,9,525) $\cup$ 5-(20,10,1155) \cite{TranvanTrung86}

516 5-(22,11,1680) (complement has $\lambda=10696$)
Alltop construction for design number 513
PGL(3,4)+ Alltop construction from 4-(21,10,1680)
\cite{Kreher95} $PSL(3,4)+$ $PGL(2,19)++$

10841 5-(23,11,1680) (complement has $\lambda=16884$)
TvT: 5-(22,10,560) $\cup$ 5-(22,11,1120)

3474 5-(24,9,1680) (complement has $\lambda=2196$)
$M_{24}$ 1 isomorphism type

3478 5-(24,9,1686) (complement has $\lambda=2190$)
$PGL(2,23)$ (>1 isomorphism types)

3482 5-(24,9,1692) (complement has $\lambda=2184$)
$PGL(2,23)$ (>1 isomorphism types)

2421 5-(24,10,1692) (complement has $\lambda=9936$)
$PSL(2,23)$

6333 5-(26,10,1701) (complement has $\lambda=18648$)
derived from number 6331

6331 6-(27,11,1701) (complement has $\lambda=18648$)
\cite{Sebille98} $AGL(3,3)$

3486 5-(24,9,1710) (complement has $\lambda=2166$)
$PGL(2,23)$ (>1 isomorphism types)

7897 5-(25,9,1710) (complement has $\lambda=3135$)
design of number 7896 with respect to smaller t
derived from number 7902

7902 6-(26,10,1710) (complement has $\lambda=3135$)
design of number 7901 with respect to smaller t
derived from number 8376

8376 7-(27,11,1710) (complement has $\lambda=3135$)
\cite{Sebille98} $AGL(3,3)$

3490 5-(24,9,1716) (complement has $\lambda=2160$)
\cite{Driessen78} $M_{24}$ 1 isomorphism type
$PGL(2,23)$ (>1 isomorphism types)
derived from number 7953

7953 6-(25,10,1716) (complement has $\lambda=2160$)
derived from number 7951

7951 7-(26,11,1716) (complement has $\lambda=2160$)
$P\Gamma L(2,25)$(>=1 isom. type)

5590 5-(22,10,1722) (complement has $\lambda=4466$)
derived from number 5587

5587 6-(23,11,1722) (complement has $\lambda=4466$)
PSL(2,19)+++ (>=1 isom. types)
derived from number 5593

5593 7-(24,12,1722) (complement has $\lambda=4466$)
Alltop construction for design number 5587

3494 5-(24,9,1728) (complement has $\lambda=2148$)
$PGL(2,23)$ (>1 isomorphism types)
residual design of number 10488
derived from number 10489

8020 5-(25,10,1728) (complement has $\lambda=13776$)
residual design of number 8017
derived from number 8018

10489 6-(25,10,1728) (complement has $\lambda=2148$)
residual design of number 10486
derived from number 10487

8018 6-(26,11,1728) (complement has $\lambda=13776$)
residual design of number 8016

10487 7-(26,11,1728) (complement has $\lambda=2148$)
residual design of number 10485

3497 5-(24,9,1740) (complement has $\lambda=2136$)
$PSL(2,23)$ (>1 isomorphism types)

8381 5-(25,9,1740) (complement has $\lambda=3105$)
derived from number 8379

8379 6-(26,10,1740) (complement has $\lambda=3105$)
derived from number 8378

8378 7-(27,11,1740) (complement has $\lambda=3105$)
\cite{Sebille98} $AGL(3,3)$

3501 5-(24,9,1746) (complement has $\lambda=2130$)
$PSL(2,23)$ (>1 isomorphism types)

3505 5-(24,9,1752) (complement has $\lambda=2124$)
$PGL(2,23)$ (>1 isomorphism types)

8395 5-(25,9,1755) (complement has $\lambda=3090$)
derived from number 8390

8390 6-(26,10,1755) (complement has $\lambda=3090$)
derived from number 8388

8388 7-(27,11,1755) (complement has $\lambda=3090$)
$ASL(3,3)$

2130 5-(22,11,1764) (complement has $\lambda=10612$)
Alltop construction for design number 2127
$PGL(2,19)++$

11023 5-(23,11,1764) (complement has $\lambda=16800$)
TvT: 5-(22,10,588) $\cup$ 5-(22,11,1176)

2425 5-(24,10,1764) (complement has $\lambda=9864$)
$PSL(2,23)$

7338 5-(29,9,1764) (complement has $\lambda=8862$)
design of number 7337 with respect to smaller t
derived from number 7464
residual design of number 7558

7464 6-(30,10,1764) (complement has $\lambda=8862$)
$P\Gamma L(2,27)++$ (many isom. types) \cite{Bettenetal97b}

3509 5-(24,9,1776) (complement has $\lambda=2100$)
$PSL(2,23)$ (>1 isomorphism types)

2429 5-(24,10,1782) (complement has $\lambda=9846$)
$PSL(2,23)$

6315 5-(25,9,1785) (complement has $\lambda=3060$)
residual design of number 6314
design of number 8004 with respect to smaller t
derived from number 8408

8408 6-(26,10,1785) (complement has $\lambda=3060$)
derived from number 8407

8407 7-(27,11,1785) (complement has $\lambda=3060$)
\cite{Sebille98} $AGL(3,3)$

3513 5-(24,9,1788) (complement has $\lambda=2088$)
$PGL(2,23)$ (>1 isomorphism types)

2137 5-(22,11,1792) (complement has $\lambda=10584$)
Alltop construction for design number 2134
\cite{Kreher95}

7556 5-(30,9,1800) (complement has $\lambda=10850$)
design of number 7555 with respect to smaller t
derived from number 7578

7578 6-(31,10,1800) (complement has $\lambda=10850$)
(Tran van Trung construction): 6-(30,9,288) together with 6-(30,10,1512) \cite{Bettenetal97b}

10844 5-(23,11,1806) (complement has $\lambda=16758$)
TvT: 5-(22,10,602) $\cup$ 5-(22,11,1204)

3519 5-(24,9,1806) (complement has $\lambda=2070$)
$PGL(2,23)$ (>1 isomorphism types)

3523 5-(24,9,1812) (complement has $\lambda=2064$)
$PGL(2,23)$ (>1 isomorphism types)

3527 5-(24,9,1824) (complement has $\lambda=2052$)
$PGL(2,23)$ (>1 isomorphism types)
design of number 7887 with respect to smaller t
derived from number 7892
residual design of number 7899

11034 5-(25,10,1824) (complement has $\lambda=13680$)
TvT: 5-(24,9,456) $\cup$ 5-(24,10,1368)

7892 6-(25,10,1824) (complement has $\lambda=2052$)
design of number 7891 with respect to smaller t
residual design of number 7903

3531 5-(24,9,1830) (complement has $\lambda=2046$)
$PGL(2,23)$ (>1 isomorphism types)

3535 5-(24,9,1836) (complement has $\lambda=2040$)
$PGL(2,23)$ (>1 isomorphism types)
residual design of number 8008

3538 5-(24,9,1842) (complement has $\lambda=2034$)
$PGL(2,23)$ (>1 isomorphism types)

8417 5-(25,9,1845) (complement has $\lambda=3000$)
derived from number 8415

8415 6-(26,10,1845) (complement has $\lambda=3000$)
derived from number 8414

8414 7-(27,11,1845) (complement has $\lambda=3000$)
\cite{Sebille98} $AGL(3,3)$

1861 5-(21,10,1848) (complement has $\lambda=2520$)
$PGL(2,19)+$
derived from number 5573

1850 5-(21,11,1848) (complement has $\lambda=6160$)
supplementary design of number 1849
residual design of number 5571
design of number 5577 with respect to smaller t

2285 5-(22,11,1848) (complement has $\lambda=10528$)
\cite{Kreher95}
Alltop construction for design number 2287

5573 6-(22,11,1848) (complement has $\lambda=2520$)
$PGL(2,19)++$

3541 5-(24,9,1848) (complement has $\lambda=2028$)
$PGL(2,23)$ (>1 isomorphism types)

3544 5-(24,9,1860) (complement has $\lambda=2016$)
$M_{11}_{12}\times id_2$
$PSL(2,23)$ (>1 isomorphism types)

3548 5-(24,9,1872) (complement has $\lambda=2004$)
$PGL(2,23)$ (>1 isomorphism types)

8430 5-(25,9,1875) (complement has $\lambda=2970$)
derived from number 8425

8425 6-(26,10,1875) (complement has $\lambda=2970$)
derived from number 8423

8423 7-(27,11,1875) (complement has $\lambda=2970$)
$ASL(3,3)$

2144 5-(22,11,1876) (complement has $\lambda=10500$)
Alltop construction for design number 2141

3552 5-(24,9,1878) (complement has $\lambda=1998$)
$PGL(2,23)$ (>1 isomorphism types)

2212 5-(22,10,1890) (complement has $\lambda=4298$)
$PGL(2,19)++$

10966 5-(23,11,1890) (complement has $\lambda=16674$)
TvT: 5-(22,10,630) $\cup$ 5-(22,11,1260)

8444 5-(25,9,1890) (complement has $\lambda=2955$)
derived from number 8439

6310 5-(26,9,1890) (complement has $\lambda=4095$)
design of number 6309 with respect to smaller t
residual design of number 8814

8439 6-(26,10,1890) (complement has $\lambda=2955$)
derived from number 8437

6844 5-(27,9,1890) (complement has $\lambda=5425$)
derived from number 6842

8437 7-(27,11,1890) (complement has $\lambda=2955$)
$ASL(3,3)$

6842 6-(28,10,1890) (complement has $\lambda=5425$)
$P\Gamma L(2,27)$

3556 5-(24,9,1896) (complement has $\lambda=1980$)
$PGL(2,23)$ (>1 isomorphism types)
derived from number 7959

8597 5-(25,10,1896) (complement has $\lambda=13608$)
derived from number 8592

7959 6-(25,10,1896) (complement has $\lambda=1980$)
derived from number 7957

8592 6-(26,11,1896) (complement has $\lambda=13608$)
derived from number 8590

7957 7-(26,11,1896) (complement has $\lambda=1980$)
$P\Gamma L(2,25)$(>=1 isom. type)

8590 7-(27,12,1896) (complement has $\lambda=13608$)
$ASL(3,3)$ 632 isomorphism types

3560 5-(24,9,1902) (complement has $\lambda=1974$)
$PGL(2,23)$ (>1 isomorphism types)

2219 5-(22,10,1904) (complement has $\lambda=4284$)
\cite{Kreher95}
TvT: 5-(21,9,560) $\cup$ 5-(21,10,1344)

1836 5-(22,11,1904) (complement has $\lambda=10472$)
Tran van Trung construction with supplementary design for design number 1833
Alltop construction for design number 1835
\cite{Kreher95}

3564 5-(24,9,1908) (complement has $\lambda=1968$)
$PGL(2,23)$ (>1 isomorphism types)

3567 5-(24,9,1914) (complement has $\lambda=1962$)
$PGL(2,23)$ (>1 isomorphism types)

3571 5-(24,9,1920) (complement has $\lambda=1956$)
$PGL(2,23)$ (>1 isomorphism types)

8459 5-(25,9,1920) (complement has $\lambda=2925$)
derived from number 8458

8458 6-(26,10,1920) (complement has $\lambda=2925$)
derived from number 8457

8457 7-(27,11,1920) (complement has $\lambda=2925$)
\cite{Sebille98} $AGL(3,3)$

3574 5-(24,9,1926) (complement has $\lambda=1950$)
$PGL(2,23)$ (>1 isomorphism types)
derived from number 7965

7965 6-(25,10,1926) (complement has $\lambda=1950$)
derived from number 7963

7963 7-(26,11,1926) (complement has $\lambda=1950$)
$P\Gamma L(2,25)$(>=1 isom. type)

2153 5-(22,11,1932) (complement has $\lambda=10444$)
Alltop construction for design number 2150

3578 5-(24,9,1932) (complement has $\lambda=1944$)
$PGL(2,23)$ (>1 isomorphism types)
derived from number 10517

10517 6-(25,10,1932) (complement has $\lambda=1944$)
derived from number 10516

10516 7-(26,11,1932) (complement has $\lambda=1944$)
derived from number 10515

10515 8-(27,12,1932) (complement has $\lambda=1944$)
$ASL(3,3)$

7344 5-(29,9,1932) (complement has $\lambda=8694$)
design of number 7343 with respect to smaller t

3582 5-(24,9,1938) (selfcomplementary)
$PSL(2,23)$ (>1 isomorphism types) halving of complete design!
design of number 5787 with respect to smaller t
complementary design of number 5787 with respect to smaller t
derived from number 5788
derived from complement of number 5788

5788 6-(25,10,1938) (selfcomplementary)
TvT: 6-(24,9,408) $\cup$ 6-(24,10,1530) Halving of the complete design

10833 5-(23,12,1944) (complement has $\lambda=29880$)
supplementary design of number 10832

8618 5-(25,10,1944) (complement has $\lambda=13560$)
derived from number 8616

8616 6-(26,11,1944) (complement has $\lambda=13560$)
derived from number 8615

8615 7-(27,12,1944) (complement has $\lambda=13560$)
$ASL(3,3)$ 1782 isomorphism types

7642 5-(31,9,1950) (complement has $\lambda=13000$)
design of number 7641 with respect to smaller t

2160 5-(22,11,1960) (complement has $\lambda=10416$)
Alltop construction for design number 2157
\cite{Kreher95}

7703 5-(36,8,1975) (complement has $\lambda=2520$)
derived from number 7701

7701 6-(37,9,1975) (complement has $\lambda=2520$)
$Sp(6,2)_36+$ (many isom. types)

8464 5-(25,9,1980) (complement has $\lambda=2865$)
derived from number 8462

8462 6-(26,10,1980) (complement has $\lambda=2865$)
derived from number 8461

8461 7-(27,11,1980) (complement has $\lambda=2865$)
\cite{Sebille98} $AGL(3,3)$

3883 5-(25,9,1995) (complement has $\lambda=2850$)
TvT: 5-(24,8,399) $\cup$ 5-(24,9,1596)

9185 5-(27,9,1995) (complement has $\lambda=5320$)
residual design of number 9182
derived from number 9183

9183 6-(28,10,1995) (complement has $\lambda=5320$)
residual design of number 9180

8476 5-(25,9,2010) (complement has $\lambda=2835$)
derived from number 8471

8471 6-(26,10,2010) (complement has $\lambda=2835$)
derived from number 8469

8469 7-(27,11,2010) (complement has $\lambda=2835$)
$ASL(3,3)$

1870 5-(21,10,2016) (complement has $\lambda=2352$)
$PGL(2,19)+$
residual design of number 5569
derived from number 5574
design of number 5581 with respect to smaller t

2167 5-(22,11,2016) (complement has $\lambda=10360$)
Alltop construction for design number 2164
\cite{Kreher95}

5574 6-(22,11,2016) (complement has $\lambda=2352$)
$PGL(2,19)++$
design of number 5580 with respect to smaller t
Tran van Trung construction with supplementary design for design number 5581

2328 5-(23,11,2016) (complement has $\lambda=16548$)
TvT: 5-(22,10,672) $\cup$ 5-(22,11,1344)

10961 5-(23,12,2016) (complement has $\lambda=29808$)
supplementary design of number 10960

8490 5-(25,9,2025) (complement has $\lambda=2820$)
derived from number 8488

8488 6-(26,10,2025) (complement has $\lambda=2820$)
derived from number 8487

8487 7-(27,11,2025) (complement has $\lambda=2820$)
\cite{Sebille98} $AGL(3,3)$

7351 5-(28,9,2030) (complement has $\lambda=6825$)
residual design of number 7348

3886 5-(25,9,2040) (complement has $\lambda=2805$)
TvT: 5-(24,8,408) $\cup$ 5-(24,9,1632)

2174 5-(22,11,2044) (complement has $\lambda=10332$)
Alltop construction for design number 2171

2441 5-(24,10,2052) (complement has $\lambda=9576$)
$PSL(2,23)$ (many isomorphism types)

8499 5-(25,9,2055) (complement has $\lambda=2790$)
derived from number 8497

8497 6-(26,10,2055) (complement has $\lambda=2790$)
derived from number 8496

8496 7-(27,11,2055) (complement has $\lambda=2790$)
\cite{Sebille98} $AGL(3,3)$

10969 5-(23,11,2058) (complement has $\lambda=16506$)
TvT: 5-(22,10,686) $\cup$ 5-(22,11,1372)

6343 5-(26,10,2079) (complement has $\lambda=18270$)
derived from number 6341

6341 6-(27,11,2079) (complement has $\lambda=18270$)
\cite{Sebille98} $AGL(3,3)$

2445 5-(24,10,2088) (complement has $\lambda=9540$)
$PSL(2,23)$ (many isomorphism types)

2181 5-(22,11,2100) (complement has $\lambda=10276$)
Alltop construction for design number 2178
$PGL(2,19)++$

4462 5-(28,9,2100) (complement has $\lambda=6755$)
$Sp(6,2)$ (2 isom. types)

7559 5-(30,9,2100) (complement has $\lambda=10550$)
design of number 7558 with respect to smaller t
derived from number 7581

7581 6-(31,10,2100) (complement has $\lambda=10550$)
(Tran van Trung construction): 6-(30,9,336) together with 6-(30,10,1764) \cite{Bettenetal97b}

3997 5-(27,12,2112) (complement has $\lambda=168432$)
TvT: 5-(26,11,672) $\cup$ 5-(26,12,1440)

8513 5-(25,9,2115) (complement has $\lambda=2730$)
derived from number 8508

8508 6-(26,10,2115) (complement has $\lambda=2730$)
derived from number 8506

8506 7-(27,11,2115) (complement has $\lambda=2730$)
$ASL(3,3)$

552 5-(22,11,2128) (complement has $\lambda=10248$)
Alltop construction for design number 549
PGL(3,4)+ Alltop construction from 4-(21,10,2128)

9197 5-(27,9,2130) (complement has $\lambda=5185$)
derived from number 9192

9192 6-(28,10,2130) (complement has $\lambda=5185$)
derived from number 9190

9190 7-(29,11,2130) (complement has $\lambda=5185$)
$P\Gamma L(2,27)+$ (>= 1 isom. types)

5610 5-(22,10,2142) (complement has $\lambda=4046$)
derived from number 5607

5607 6-(23,11,2142) (complement has $\lambda=4046$)
PSL(2,19)+++ (>=1 isom. types)
derived from number 5612

5612 7-(24,12,2142) (complement has $\lambda=4046$)
Alltop construction for design number 5607

8527 5-(25,9,2145) (complement has $\lambda=2700$)
derived from number 8526

8526 6-(26,10,2145) (complement has $\lambda=2700$)
derived from number 8525

8525 7-(27,11,2145) (complement has $\lambda=2700$)
\cite{Sebille98} $AGL(3,3)$

4149 5-(28,10,2149) (complement has $\lambda=31500$)
\cite{Sebille98} $Sp(6,2)$ 1 isomorphism type

10836 5-(23,12,2160) (complement has $\lambda=29664$)
supplementary design of number 10835

3889 5-(25,9,2160) (complement has $\lambda=2685$)
TvT: 5-(24,8,432) $\cup$ 5-(24,9,1728)
derived from number 8530
design of number 10488 with respect to smaller t

8033 5-(25,10,2160) (complement has $\lambda=13344$)
residual design of number 8027
derived from number 8028

8530 6-(26,10,2160) (complement has $\lambda=2685$)
derived from number 8529
design of number 10486 with respect to smaller t

8028 6-(26,11,2160) (complement has $\lambda=13344$)
residual design of number 8025

8529 7-(27,11,2160) (complement has $\lambda=2685$)
\cite{Sebille98} $AGL(3,3)$
design of number 10485 with respect to smaller t

6854 5-(27,9,2170) (complement has $\lambda=5145$)
derived from number 6852

6852 6-(28,10,2170) (complement has $\lambda=5145$)
$P\Gamma L(2,27)$

1816 5-(21,10,2184) (selfcomplementary)
$PSL(3,2)\times S_3$ Halving of the complete design
derived from number 1822
derived from complement of number 1822

7836 5-(22,10,2184) (complement has $\lambda=4004$)
residual design of number 7832

2289 5-(22,11,2184) (complement has $\lambda=10192$)
\cite{Kreher95}
Alltop construction for design number 2291

1822 6-(22,11,2184) (selfcomplementary)
Alltop construction for design number 1816
Alltop

10847 5-(23,11,2184) (complement has $\lambda=16380$)
TvT: 5-(22,10,728) $\cup$ 5-(22,11,1456)

8539 5-(25,9,2190) (complement has $\lambda=2655$)
derived from number 8537

8537 6-(26,10,2190) (complement has $\lambda=2655$)
derived from number 8536

8536 7-(27,11,2190) (complement has $\lambda=2655$)
\cite{Sebille98} $AGL(3,3)$

7713 5-(36,8,2200) (complement has $\lambda=2295$)
derived from number 7711

7711 6-(37,9,2200) (complement has $\lambda=2295$)
$Sp(6,2)_36+$ (many isom. types)

255 5-(26,9,2205) (complement has $\lambda=3780$)
derived from number 253
$PGL(2,25)$
design of number 6314 with respect to smaller t
residual design of number 6831

6864 5-(27,9,2205) (complement has $\lambda=5110$)
derived from number 6862

253 6-(27,10,2205) (complement has $\lambda=3780$)
$ASL(3,3)^{13}$
TvT: 6-(26,9,420) $\cup$ 6-(26,10,1785)
\cite{Sebille98} $AGL(3,3)$

6862 6-(28,10,2205) (complement has $\lambda=5110$)
$P\Gamma L(2,27)$

5621 5-(22,10,2226) (complement has $\lambda=3962$)
derived from number 5618

5618 6-(23,11,2226) (complement has $\lambda=3962$)
PSL(2,19)+++ (>=1 isom. types)
derived from number 5624

5624 7-(24,12,2226) (complement has $\lambda=3962$)
Alltop construction for design number 5618

4466 5-(28,9,2240) (complement has $\lambda=6615$)
$Sp(6,2)$ (2 isom. types)
residual design of number 7358

8552 5-(25,9,2250) (complement has $\lambda=2595$)
derived from number 8547

8547 6-(26,10,2250) (complement has $\lambda=2595$)
derived from number 8545

8545 7-(27,11,2250) (complement has $\lambda=2595$)
$ASL(3,3)$

11026 5-(23,11,2268) (complement has $\lambda=16296$)
TvT: 5-(22,10,756) $\cup$ 5-(22,11,1512)

6353 5-(26,10,2268) (complement has $\lambda=18081$)
derived from number 6351
design of number 8017 with respect to smaller t

6351 6-(27,11,2268) (complement has $\lambda=18081$)
\cite{Sebille98} $AGL(3,3)$
design of number 8016 with respect to smaller t

7900 5-(25,9,2280) (complement has $\lambda=2565$)
design of number 7899 with respect to smaller t
derived from number 7904

7904 6-(26,10,2280) (complement has $\lambda=2565$)
design of number 7903 with respect to smaller t
derived from number 8563

8563 7-(27,11,2280) (complement has $\lambda=2565$)
\cite{Sebille98} $AGL(3,3)$

277 5-(25,9,2295) (complement has $\lambda=2550$)
residual design of number 274
derived from number 275
design of number 8008 with respect to smaller t

275 6-(26,10,2295) (complement has $\lambda=2550$)
residual design of number 273
derived from number 8565

8565 7-(27,11,2295) (complement has $\lambda=2550$)
\cite{Sebille98} $AGL(3,3)$

480 5-(22,11,2296) (complement has $\lambda=10080$)
Alltop construction for design number 477
$PSL(3,4)+$
\cite{Kreher95}
PSL(3,4)+ Alltop construction from 4-(21,10,2296)

42 5-(30,9,2300) (complement has $\lambda=10350$)
TvT: 5-(29,8,368) $\cup$ 5-(29,9,1932)

10432 5-(38,8,2304) (complement has $\lambda=3152$)
derived from number 10427

10427 6-(39,9,2304) (complement has $\lambda=3152$)
derived from number 10425

10425 7-(40,10,2304) (complement has $\lambda=3152$)
$PSL(4,3)$ (many isomorphism types)

5583 5-(20,11,2310) (complement has $\lambda=2695$)
residual design of number 5582

10850 5-(23,11,2310) (complement has $\lambda=16254$)
TvT: 5-(22,10,770) $\cup$ 5-(22,11,1540)

2669 5-(24,11,2310) (complement has $\lambda=24822$)
\cite{Bluskov}

8815 5-(27,9,2310) (complement has $\lambda=5005$)
design of number 8814 with respect to smaller t

8572 5-(25,9,2325) (complement has $\lambda=2520$)
derived from number 8570

8570 6-(26,10,2325) (complement has $\lambda=2520$)
derived from number 8569

8569 7-(27,11,2325) (complement has $\lambda=2520$)
\cite{Sebille98} $AGL(3,3)$

7364 5-(28,9,2345) (complement has $\lambda=6510$)
residual design of number 7361

468 5-(22,11,2352) (complement has $\lambda=10024$)
Alltop construction for design number 465
$PSL(3,4)+$
\cite{Kreher95}
PSL(3,4)+ Alltop construction from 4-(21,10,2352)

11021 5-(23,12,2376) (complement has $\lambda=29448$)
supplementary design of number 11020

2221 5-(22,10,2380) (complement has $\lambda=3808$)
\cite{Kreher95}
TvT: 5-(21,9,700) $\cup$ 5-(21,10,1680)

1845 5-(22,11,2380) (complement has $\lambda=9996$)
Tran van Trung construction with supplementary design for design number 1840
Alltop construction for design number 1842
\cite{Kreher95}
design of number 5570 with respect to smaller t
residual design of number 11494
derived from number 11495

11495 6-(23,12,2380) (complement has $\lambda=9996$)
supplementary design of number 11494
residual design of number 11497

8581 5-(25,9,2385) (complement has $\lambda=2460$)
derived from number 8579

8579 6-(26,10,2385) (complement has $\lambda=2460$)
derived from number 8578

8578 7-(27,11,2385) (complement has $\lambda=2460$)
\cite{Sebille98} $AGL(3,3)$

10972 5-(23,11,2394) (complement has $\lambda=16170$)
TvT: 5-(22,10,798) $\cup$ 5-(22,11,1596)

11033 5-(24,11,2394) (complement has $\lambda=24738$)
TvT: 5-(23,10,756) $\cup$ 5-(23,11,1638)

8588 5-(25,9,2415) (complement has $\lambda=2430$)
derived from number 8586

8586 6-(26,10,2415) (complement has $\lambda=2430$)
derived from number 8585

8585 7-(27,11,2415) (complement has $\lambda=2430$)
\cite{Sebille98} $AGL(3,3)$

4470 5-(28,9,2415) (complement has $\lambda=6440$)
$Sp(6,2)$ (5 isom. types)
residual design of number 7371
derived from number 9181
design of number 9182 with respect to smaller t

9181 6-(29,10,2415) (complement has $\lambda=6440$)
design of number 9180 with respect to smaller t

10853 5-(23,11,2436) (complement has $\lambda=16128$)
TvT: 5-(22,10,812) $\cup$ 5-(22,11,1624)

7349 5-(29,9,2436) (complement has $\lambda=8190$)
design of number 7348 with respect to smaller t

2322 5-(23,12,2448) (complement has $\lambda=29376$)
supplementary design of number 2321

8051 5-(25,10,2448) (complement has $\lambda=13056$)
residual design of number 8047
derived from number 8048

8048 6-(26,11,2448) (complement has $\lambda=13056$)
residual design of number 8045

1803 5-(21,11,2464) (complement has $\lambda=5544$)
supplementary design of number 1802

7733 5-(37,8,2480) (selfcomplementary)
residual design of number 7731
residual design of complement of number 7731

10452 5-(38,8,2504) (complement has $\lambda=2952$)
derived from number 10447

10447 6-(39,9,2504) (complement has $\lambda=2952$)
derived from number 10445

10445 7-(40,10,2504) (complement has $\lambda=2952$)
$PSL(4,3)$ (many isomorphism types)

10733 5-(24,12,2508) (complement has $\lambda=47880$)
Alltop construction for design number 10730
Tran van Trung construction with supplementary design for design number 10829

2223 5-(22,10,2520) (complement has $\lambda=3668$)
$PGL(2,19)++$

2188 5-(22,11,2520) (complement has $\lambda=9856$)
Alltop construction for design number 2185
\cite{Kreher95} $PGL(2,19)++$

11046 5-(23,11,2520) (complement has $\lambda=16044$)
TvT: 5-(22,10,840) $\cup$ 5-(22,11,1680)

3978 5-(26,9,2520) (complement has $\lambda=3465$)
TvT: 5-(25,8,480) $\cup$ 5-(25,9,2040)

3843 5-(26,13,2520) (complement has $\lambda=200970$)
Tran van Trung construction with supplementary design for design number 3840
Alltop construction for design number 3842

6874 5-(27,9,2520) (complement has $\lambda=4795$)
derived from number 6872

4472 5-(28,9,2520) (complement has $\lambda=6335$)
$Sp(6,2)$ (5 isom. types)
residual design of number 7372

6872 6-(28,10,2520) (complement has $\lambda=4795$)
$P\Gamma L(2,27)$

9288 5-(29,9,2520) (complement has $\lambda=8106$)
residual design of number 9282
derived from number 9283

9283 6-(30,10,2520) (complement has $\lambda=8106$)
residual design of number 9280

2460 5-(24,10,2538) (complement has $\lambda=9090$)
$PSL(2,23)$

8630 5-(25,10,2544) (complement has $\lambda=12960$)
derived from number 8628

8628 6-(26,11,2544) (complement has $\lambda=12960$)
derived from number 8627

8627 7-(27,12,2544) (complement has $\lambda=12960$)
\cite{Sebille98} $AGL(3,3)$ 1 isomorphism type

4476 5-(28,9,2555) (complement has $\lambda=6300$)
$Sp(6,2)$ (3 isom. types)

2230 5-(22,10,2562) (complement has $\lambda=3626$)
$PGL(2,19)++$

6884 5-(27,9,2590) (complement has $\lambda=4725$)
derived from number 6882

6882 6-(28,10,2590) (complement has $\lambda=4725$)
$P\Gamma L(2,27)$

8064 5-(25,10,2592) (complement has $\lambda=12912$)
residual design of number 8059
derived from number 8060

8060 6-(26,11,2592) (complement has $\lambda=12912$)
residual design of number 8057
derived from number 8639

8639 7-(27,12,2592) (complement has $\lambda=12912$)
\cite{Sebille98} $AGL(3,3)$ 33 isomorphism types

7742 5-(39,8,2592) (complement has $\lambda=3392$)
derived from number 7740

7740 6-(40,9,2592) (complement has $\lambda=3392$)
$PSL(4,3)$

7752 5-(39,8,2600) (complement has $\lambda=3384$)
derived from number 7750

7750 6-(40,9,2600) (complement has $\lambda=3384$)
$PSL(4,3)$

2195 5-(22,11,2604) (complement has $\lambda=9772$)
Alltop construction for design number 2192
$PGL(2,19)++$

2293 5-(22,11,2632) (complement has $\lambda=9744$)
\cite{Kreher95}
Alltop construction for design number 2295

10856 5-(23,11,2646) (complement has $\lambda=15918$)
TvT: 5-(22,10,882) $\cup$ 5-(22,11,1764)

6363 5-(26,10,2646) (complement has $\lambda=17703$)
derived from number 6361

6361 6-(27,11,2646) (complement has $\lambda=17703$)
\cite{Sebille98} $AGL(3,3)$

4479 5-(28,9,2660) (complement has $\lambda=6195$)
$Sp(6,2)$ (7 isom. types)
residual design of number 7378

10839 5-(23,12,2664) (complement has $\lambda=29160$)
supplementary design of number 10838

532 5-(22,11,2688) (complement has $\lambda=9688$)
Alltop construction for design number 529
\cite{Kreher95}
PGL(3,4)+ Alltop construction from 4-(21,10,2688)

10975 5-(23,11,2688) (complement has $\lambda=15876$)
TvT: 5-(22,10,896) $\cup$ 5-(22,11,1792)

8081 5-(25,10,2688) (complement has $\lambda=12816$)
residual design of number 8075
derived from number 8076

8076 6-(26,11,2688) (complement has $\lambda=12816$)
residual design of number 8073

7359 5-(29,9,2688) (complement has $\lambda=7938$)
design of number 7358 with respect to smaller t
derived from number 7470
residual design of number 7561

7470 6-(30,10,2688) (complement has $\lambda=7938$)
$P\Gamma L(2,27)++$ (many isom. types) \cite{Bettenetal97b}

4137 5-(27,9,2695) (complement has $\lambda=4620$)
TvT: 5-(26,8,490) $\cup$ 5-(26,9,2205)
design of number 6831 with respect to smaller t
derived from number 6892

6892 6-(28,10,2695) (complement has $\lambda=4620$)
TvT: 6-(27,9,490) $\cup$ 6-(27,10,2205)

7732 5-(38,8,2728) (selfcomplementary)
design of number 7731 with respect to smaller t
complementary design of number 7731 with respect to smaller t
residual design of number 7737
residual design of complement of number 7737

2237 5-(22,10,2730) (complement has $\lambda=3458$)
$PGL(2,19)++$

7762 5-(39,8,2736) (complement has $\lambda=3248$)
derived from number 7760

7760 6-(40,9,2736) (complement has $\lambda=3248$)
$PSL(4,3)$

7772 5-(39,8,2744) (complement has $\lambda=3240$)
derived from number 7770

7770 6-(40,9,2744) (complement has $\lambda=3240$)
$PSL(4,3)$

1853 5-(21,11,2772) (complement has $\lambda=5236$)
supplementary design of number 1852
residual design of number 5572

2243 5-(22,10,2772) (complement has $\lambda=3416$)
$PGL(2,19)++$

2202 5-(22,11,2772) (complement has $\lambda=9604$)
Alltop construction for design number 2199

5665 5-(23,10,2772) (complement has $\lambda=5796$)
derived from number 5663

5663 6-(24,11,2772) (complement has $\lambda=5796$)
PSL(2,23) (>=1 isom. types)

836 5-(25,10,2784) (complement has $\lambda=12720$)
TvT: 5-(24,9,696) $\cup$ 5-(24,10,2088)

6895 5-(27,9,2800) (complement has $\lambda=4515$)
derived from number 6893

6893 6-(28,10,2800) (complement has $\lambda=4515$)
$P\Gamma L(2,27)$

10964 5-(23,12,2808) (complement has $\lambda=29016$)
supplementary design of number 10963

10859 5-(23,11,2814) (complement has $\lambda=15750$)
TvT: 5-(22,10,938) $\cup$ 5-(22,11,1876)

7362 5-(29,9,2814) (complement has $\lambda=7812$)
design of number 7361 with respect to smaller t

265 5-(26,9,2835) (complement has $\lambda=3150$)
derived from number 263
design of number 274 with respect to smaller t
$PGL(2,25)$
residual design of number 8819

8030 5-(26,10,2835) (complement has $\lambda=17514$)
derived from number 8026
design of number 8027 with respect to smaller t

263 6-(27,10,2835) (complement has $\lambda=3150$)
$ASL(3,3)^{13}$
design of number 273 with respect to smaller t
\cite{Sebille98} $AGL(3,3)$
residual design of number 8817
derived from number 8824

8026 6-(27,11,2835) (complement has $\lambda=17514$)
design of number 8025 with respect to smaller t

4483 5-(28,9,2835) (complement has $\lambda=6020$)
$Sp(6,2)$ (11 isom. types)

8824 7-(28,11,2835) (complement has $\lambda=3150$)
TvT: 7-(27,10,540) $\cup$ 7-(27,11,2295)

2246 5-(22,10,2856) (complement has $\lambda=3332$)
TvT: 5-(21,9,840) $\cup$ 5-(21,10,2016)
\cite{Kreher95}
design of number 5569 with respect to smaller t
derived from number 11500

472 5-(22,11,2856) (complement has $\lambda=9520$)
Alltop construction for design number 469
Tran van Trung construction with supplementary design for design number 1849
\cite{Kreher95} $PSL(3,4)+$ Alltop construction from 4-(21,10,2856)
design of number 5571 with respect to smaller t

2335 5-(23,11,2856) (complement has $\lambda=15708$)
TvT: 5-(22,10,952) $\cup$ 5-(22,11,1904)

11500 6-(23,11,2856) (complement has $\lambda=3332$)
TvT: 6-(22,10,840) $\cup$ 6-(22,11,2016)
derived from number 11503

11503 7-(24,12,2856) (complement has $\lambda=3332$)
Alltop construction for design number 11500

10842 5-(23,12,2880) (complement has $\lambda=28944$)
supplementary design of number 10841

8100 5-(25,10,2880) (complement has $\lambda=12624$)
residual design of number 8094
derived from number 8095

8095 6-(26,11,2880) (complement has $\lambda=12624$)
residual design of number 8092

2248 5-(22,10,2898) (complement has $\lambda=3290$)
$PGL(2,19)++$

10862 5-(23,11,2898) (complement has $\lambda=15666$)
TvT: 5-(22,10,966) $\cup$ 5-(22,11,1932)

35 5-(29,9,2898) (complement has $\lambda=7728$)
residual design of number 34
derived from number 4192
design of number 7371 with respect to smaller t

4192 6-(30,10,2898) (complement has $\lambda=7728$)
\cite{Sebille98} $P\Gamma L(2,27)\cup S_2$
\cite{Sebille98} $P\Gamma L(2,27)\cup S_2$
TvT: 6-(29,9,483) $\cup$ 6-(29,10,2415)

6905 5-(27,9,2905) (complement has $\lambda=4410$)
derived from number 6903

6903 6-(28,10,2905) (complement has $\lambda=4410$)
$P\Gamma L(2,27)$

2255 5-(22,10,2912) (complement has $\lambda=3276$)
$PGL(2,19)++$
residual design of number 7840

11029 5-(23,11,2940) (complement has $\lambda=15624$)
TvT: 5-(22,10,980) $\cup$ 5-(22,11,1960)

6915 5-(27,9,2940) (complement has $\lambda=4375$)
derived from number 6913

4153 5-(28,10,2940) (complement has $\lambda=30709$)
\cite{Sebille98} $Sp(6,2)$ 1-3 isomorphism types

6913 6-(28,10,2940) (complement has $\lambda=4375$)
$P\Gamma L(2,27)$

4487 5-(28,9,2975) (complement has $\lambda=5880$)
$Sp(6,2)$ (8 isom. types)
residual design of number 7384

8120 5-(25,10,2976) (complement has $\lambda=12528$)
residual design of number 8114
derived from number 8115

8115 6-(26,11,2976) (complement has $\lambda=12528$)
residual design of number 8112

5641 5-(22,10,2982) (complement has $\lambda=3206$)
derived from number 5638

5638 6-(23,11,2982) (complement has $\lambda=3206$)
PSL(2,19)+++ (>=1 isom. types)
derived from number 5644

5644 7-(24,12,2982) (complement has $\lambda=3206$)
Alltop construction for design number 5638

4157 5-(28,10,2989) (complement has $\lambda=30660$)
\cite{Sebille98} $Sp(6,2)$ 1 isomorphism type

9558 5-(31,9,2990) (complement has $\lambda=11960$)
residual design of number 9552

7738 5-(39,8,2992) (selfcomplementary)
design of number 7737 with respect to smaller t
complementary design of number 7737 with respect to smaller t

9285 5-(30,9,3000) (complement has $\lambda=9650$)
derived from number 9281
design of number 9282 with respect to smaller t

9281 6-(31,10,3000) (complement has $\lambda=9650$)
design of number 9280 with respect to smaller t

2211 5-(22,11,3024) (complement has $\lambda=9352$)
Alltop construction for design number 2208
$PGL(2,19)++$

7835 5-(23,10,3024) (complement has $\lambda=5544$)
residual design of number 7830
design of number 7832 with respect to smaller t

10865 5-(23,11,3024) (complement has $\lambda=15540$)
TvT: 5-(22,10,1008) $\cup$ 5-(22,11,2016)

11024 5-(23,12,3024) (complement has $\lambda=28800$)
supplementary design of number 11023

8139 5-(25,10,3024) (complement has $\lambda=12480$)
residual design of number 8133
derived from number 8134

8134 6-(26,11,3024) (complement has $\lambda=12480$)
residual design of number 8131

7373 5-(29,9,3024) (complement has $\lambda=7602$)
design of number 7372 with respect to smaller t

2472 5-(24,10,3042) (complement has $\lambda=8586$)
$PSL(2,23)$ (many isomorphism types)

10978 5-(23,11,3066) (complement has $\lambda=15498$)
TvT: 5-(22,10,1022) $\cup$ 5-(22,11,2044)

4804 5-(29,9,3066) (complement has $\lambda=7560$)
TvT: 5-(28,8,511) $\cup$ 5-(28,9,2555)

10737 5-(24,12,3078) (complement has $\lambda=47310$)
Alltop construction for design number 10734
Tran van Trung construction with supplementary design for design number 10832

1810 5-(21,11,3080) (complement has $\lambda=4928$)
supplementary design of number 1809

4140 5-(27,9,3080) (complement has $\lambda=4235$)
TvT: 5-(26,8,560) $\cup$ 5-(26,9,2520)

5586 5-(22,10,3094) (selfcomplementary)
residual design of number 5585
residual design of complement of number 5585

10845 5-(23,12,3096) (complement has $\lambda=28728$)
supplementary design of number 10844

6925 5-(27,9,3115) (complement has $\lambda=4200$)
derived from number 6923

6923 6-(28,10,3115) (complement has $\lambda=4200$)
$P\Gamma L(2,27)$

10868 5-(23,11,3150) (complement has $\lambda=15414$)
TvT: 5-(22,10,1050) $\cup$ 5-(22,11,2100)

6935 5-(27,9,3150) (complement has $\lambda=4165$)
derived from number 6933

7388 5-(28,9,3150) (complement has $\lambda=5705$)
residual design of number 7385

6933 6-(28,10,3150) (complement has $\lambda=4165$)
$P\Gamma L(2,27)$

476 5-(22,11,3192) (complement has $\lambda=9184$)
Alltop construction for design number 473
$PSL(3,4)+$
PSL(3,4)+ Alltop construction from 4-(21,10,3192)

11049 5-(24,11,3192) (complement has $\lambda=23940$)
TvT: 5-(23,10,1008) $\cup$ 5-(23,11,2184)

10903 5-(24,12,3192) (complement has $\lambda=47196$)
Alltop construction for design number 10900
Tran van Trung construction with supplementary design for design number 10960

8648 5-(25,10,3192) (complement has $\lambda=12312$)
derived from number 8646

8646 6-(26,11,3192) (complement has $\lambda=12312$)
derived from number 8645

8645 7-(27,12,3192) (complement has $\lambda=12312$)
\cite{Sebille98} $AGL(3,3)$

7379 5-(29,9,3192) (complement has $\lambda=7434$)
design of number 7378 with respect to smaller t

7562 5-(30,9,3200) (complement has $\lambda=9450$)
design of number 7561 with respect to smaller t
derived from number 7584

7584 6-(31,10,3200) (complement has $\lambda=9450$)
(Tran van Trung construction): 6-(30,9,512) together with 6-(30,10,2688) \cite{Bettenetal97b}

10536 5-(24,10,3204) (complement has $\lambda=8424$)
derived from number 10529

10529 6-(25,11,3204) (complement has $\lambda=8424$)
derived from number 10521

10521 7-(26,12,3204) (complement has $\lambda=8424$)
derived from number 10518

10518 8-(27,13,3204) (complement has $\lambda=8424$)
$ASL(3,3)$
derived from number 10524

10524 9-(28,14,3204) (complement has $\lambda=8424$)
Alltop construction for design number 10518

246 5-(26,10,3213) (complement has $\lambda=17136$)
residual design of number 243
derived from number 8046
design of number 8047 with respect to smaller t

8046 6-(27,11,3213) (complement has $\lambda=17136$)
design of number 8045 with respect to smaller t

6945 5-(27,9,3220) (complement has $\lambda=4095$)
derived from number 6943

6943 6-(28,10,3220) (complement has $\lambda=4095$)
$P\Gamma L(2,27)$

10967 5-(23,12,3240) (complement has $\lambda=28584$)
supplementary design of number 10966

10568 5-(24,10,3240) (complement has $\lambda=8388$)
derived from number 10561

10561 6-(25,11,3240) (complement has $\lambda=8388$)
derived from number 10553

10553 7-(26,12,3240) (complement has $\lambda=8388$)
derived from number 10550

10550 8-(27,13,3240) (complement has $\lambda=8388$)
$ASL(3,3)$
derived from number 10556

10556 9-(28,14,3240) (complement has $\lambda=8388$)
Alltop construction for design number 10550

6955 5-(27,9,3255) (complement has $\lambda=4060$)
derived from number 6953

10661 5-(28,9,3255) (complement has $\lambda=5600$)
residual design of number 10658
derived from number 10659

6953 6-(28,10,3255) (complement has $\lambda=4060$)
$P\Gamma L(2,27)$

10659 6-(29,10,3255) (complement has $\lambda=5600$)
residual design of number 10656

8013 5-(25,10,3264) (complement has $\lambda=12240$)
residual design of number 8011

6996 5-(27,10,3276) (complement has $\lambda=23058$)
residual design of number 6993

8159 5-(25,10,3312) (complement has $\lambda=12192$)
residual design of number 8153
derived from number 8154

8154 6-(26,11,3312) (complement has $\lambda=12192$)
residual design of number 8151

504 5-(22,11,3360) (complement has $\lambda=9016$)
Alltop construction for design number 501
\cite{Kreher95} $PSL(3,4)+$ $PGL(2,19)++$Alltop construction from 4-(21,10,3360)

4490 5-(28,9,3360) (complement has $\lambda=5495$)
$Sp(6,2)$ (10 isom. types)
residual design of number 7395

9796 5-(34,9,3360) (complement has $\lambda=20391$)
derived from number 9791

9791 6-(35,10,3360) (complement has $\lambda=20391$)
derived from number 9789

9789 7-(36,11,3360) (complement has $\lambda=20391$)
$Sp(6,2)_36$ (many isomorphism types)

1862 5-(21,11,3388) (complement has $\lambda=4620$)
supplementary design of number 1861
residual design of number 5573

8062 5-(26,10,3402) (complement has $\lambda=16947$)
derived from number 8058
design of number 8059 with respect to smaller t

8058 6-(27,11,3402) (complement has $\lambda=16947$)
design of number 8057 with respect to smaller t
derived from number 11331

11331 7-(28,12,3402) (complement has $\lambda=16947$)
TvT: 7-(27,11,810) $\cup$ 7-(27,12,2592)

10741 5-(24,12,3420) (complement has $\lambda=46968$)
Alltop construction for design number 10738
Tran van Trung construction with supplementary design for design number 10835

11035 5-(25,11,3420) (complement has $\lambda=35340$)
TvT: 5-(24,10,1026) $\cup$ 5-(24,11,2394)

6965 5-(27,9,3430) (complement has $\lambda=3885$)
derived from number 6963

6963 6-(28,10,3430) (complement has $\lambda=3885$)
$P\Gamma L(2,27)$

5591 5-(22,11,3444) (complement has $\lambda=8932$)
residual design of number 5587
derived from number 5588
Alltop construction for design number 5601

5588 6-(23,12,3444) (complement has $\lambda=8932$)
supplementary design of number 5587
residual design of number 5593

24 5-(30,9,3450) (complement has $\lambda=9200$)
TvT: 5-(29,8,552) $\cup$ 5-(29,9,2898)
design of number 34 with respect to smaller t
derived from number 37

9352 5-(31,9,3450) (complement has $\lambda=11500$)
residual design of number 9346
derived from number 9347

37 6-(31,10,3450) (complement has $\lambda=9200$)
TvT: 6-(30,9,552) $\cup$ 6-(30,10,2898)

9347 6-(32,10,3450) (complement has $\lambda=11500$)
residual design of number 9344

2329 5-(23,12,3456) (complement has $\lambda=28368$)
supplementary design of number 2328

8175 5-(25,10,3456) (complement has $\lambda=12048$)
residual design of number 8172
derived from number 8173

8173 6-(26,11,3456) (complement has $\lambda=12048$)
residual design of number 8171

8821 5-(27,9,3465) (complement has $\lambda=3850$)
derived from number 8818
design of number 8819 with respect to smaller t

7403 5-(28,9,3465) (complement has $\lambda=5390$)
residual design of number 7401

8818 6-(28,10,3465) (complement has $\lambda=3850$)
design of number 8817 with respect to smaller t
derived from number 9210

9210 7-(29,11,3465) (complement has $\lambda=3850$)
$P\Gamma L(2,27)+$ (>= 1 isom. types)

2297 5-(22,11,3472) (complement has $\lambda=8904$)
$PSL(3,4)+$
Alltop construction for design number 2299

4494 5-(28,9,3500) (complement has $\lambda=5355$)
$Sp(6,2)$ (20 isom. types)
residual design of number 10648
derived from number 10649

10649 6-(29,10,3500) (complement has $\lambda=5355$)
residual design of number 10646

9555 5-(32,9,3510) (complement has $\lambda=14040$)
residual design of number 9550
design of number 9552 with respect to smaller t

524 5-(22,11,3528) (complement has $\lambda=8848$)
Alltop construction for design number 521
PGL(3,4)+ Alltop construction from 4-(21,10,3528)

10970 5-(23,12,3528) (complement has $\lambda=28296$)
supplementary design of number 10969

7911 5-(24,10,3528) (complement has $\lambda=8100$)
residual design of number 7907
derived from number 7908

7908 6-(25,11,3528) (complement has $\lambda=8100$)
residual design of number 7905

8078 5-(26,10,3528) (complement has $\lambda=16821$)
derived from number 8074
design of number 8075 with respect to smaller t

8074 6-(27,11,3528) (complement has $\lambda=16821$)
design of number 8073 with respect to smaller t

6975 5-(27,9,3535) (complement has $\lambda=3780$)
derived from number 6973

6973 6-(28,10,3535) (complement has $\lambda=3780$)
$P\Gamma L(2,27)$

8189 5-(25,10,3552) (complement has $\lambda=11952$)
residual design of number 8183
derived from number 8184

8184 6-(26,11,3552) (complement has $\lambda=11952$)
residual design of number 8181

11484 5-(23,11,3570) (complement has $\lambda=14994$)
TvT: 5-(22,10,1190) $\cup$ 5-(22,11,2380)
design of number 11494 with respect to smaller t
derived from number 11496

11496 6-(24,12,3570) (complement has $\lambda=14994$)
Tran van Trung construction with supplementary design for design number 11494
design of number 11497 with respect to smaller t

6985 5-(27,9,3570) (complement has $\lambda=3745$)
derived from number 6983

6983 6-(28,10,3570) (complement has $\lambda=3745$)
$P\Gamma L(2,27)$

4806 5-(29,9,3570) (complement has $\lambda=7056$)
TvT: 5-(28,8,595) $\cup$ 5-(28,9,2975)
design of number 7384 with respect to smaller t
derived from number 7476
residual design of number 7564

7476 6-(30,10,3570) (complement has $\lambda=7056$)
$P\Gamma L(2,27)++$ (many isom. types) \cite{Bettenetal97b}

4497 5-(28,9,3675) (complement has $\lambda=5180$)
$Sp(6,2)$ (11 isom. types)
residual design of number 7407

9577 5-(31,9,3680) (complement has $\lambda=11270$)
residual design of number 9571

1871 5-(21,11,3696) (complement has $\lambda=4312$)
supplementary design of number 1870
residual design of number 5574
design of number 5582 with respect to smaller t

2301 5-(22,11,3696) (complement has $\lambda=8680$)
$PSL(3,4)+$
Alltop construction for design number 2303
\cite{Kreher95}

11498 5-(22,12,3740) (complement has $\lambda=15708$)
residual design of number 11495

10848 5-(23,12,3744) (complement has $\lambda=28080$)
supplementary design of number 10847

8209 5-(25,10,3744) (complement has $\lambda=11760$)
residual design of number 8203
derived from number 8204

8204 6-(26,11,3744) (complement has $\lambda=11760$)
residual design of number 8201

10998 5-(24,12,3762) (complement has $\lambda=46626$)
Alltop construction for design number 10995
Tran van Trung construction with supplementary design for design number 11020

2218 5-(22,11,3780) (complement has $\lambda=8596$)
Alltop construction for design number 2215
$PGL(2,19)++$

10828 5-(23,10,3780) (complement has $\lambda=4788$)
TvT: 5-(22,9,1050) $\cup$ 5-(22,10,2730)

10871 5-(23,11,3780) (complement has $\lambda=14784$)
TvT: 5-(22,10,1260) $\cup$ 5-(22,11,2520)

8097 5-(26,10,3780) (complement has $\lambda=16569$)
derived from number 8093
design of number 8094 with respect to smaller t

8093 6-(27,11,3780) (complement has $\lambda=16569$)
design of number 8092 with respect to smaller t

4501 5-(28,9,3780) (complement has $\lambda=5075$)
$Sp(6,2)$ (25 isom. types)
residual design of number 7410

7386 5-(29,9,3780) (complement has $\lambda=6846$)
design of number 7385 with respect to smaller t

1805 5-(22,11,3808) (complement has $\lambda=8568$)
Tran van Trung construction with supplementary design for design number 1802
Alltop construction for design number 1804
\cite{Kreher95}
Tran van Trung construction from 5-(21,10,1344)

4504 5-(28,9,3815) (complement has $\lambda=5040$)
$Sp(6,2)$ (18 isom. types)

8227 5-(25,10,3840) (complement has $\lambda=11664$)
residual design of number 8222
derived from number 8223

8223 6-(26,11,3840) (complement has $\lambda=11664$)
residual design of number 8220
derived from number 8657

8657 7-(27,12,3840) (complement has $\lambda=11664$)
\cite{Sebille98} $AGL(3,3)$

5375 5-(46,8,3840) (complement has $\lambda=6820$)
$M_{23}\times Id_2$

2324 5-(24,12,3876) (complement has $\lambda=46512$)
Tran van Trung construction with supplementary design for design number 2321
Alltop construction for design number 2323
\cite{Bluskov}

11027 5-(23,12,3888) (complement has $\lambda=27936$)
supplementary design of number 11026

10504 5-(24,10,3888) (complement has $\lambda=7740$)
residual design of number 10501
derived from number 10502

8240 5-(25,10,3888) (complement has $\lambda=11616$)
residual design of number 8237
derived from number 8238

10502 6-(25,11,3888) (complement has $\lambda=7740$)
residual design of number 10499
derived from number 10500

8238 6-(26,11,3888) (complement has $\lambda=11616$)
residual design of number 8236
derived from number 8663

10500 7-(26,12,3888) (complement has $\lambda=7740$)
residual design of number 10498

8663 7-(27,12,3888) (complement has $\lambda=11616$)
\cite{Sebille98} $AGL(3,3)$

10981 5-(23,11,3906) (complement has $\lambda=14658$)
TvT: 5-(22,10,1302) $\cup$ 5-(22,11,2604)

8117 5-(26,10,3906) (complement has $\lambda=16443$)
derived from number 8113
design of number 8114 with respect to smaller t

8113 6-(27,11,3906) (complement has $\lambda=16443$)
design of number 8112 with respect to smaller t

9307 5-(29,9,3906) (complement has $\lambda=6720$)
residual design of number 9301
derived from number 9302
design of number 10658 with respect to smaller t

9302 6-(30,10,3906) (complement has $\lambda=6720$)
residual design of number 9299
design of number 10656 with respect to smaller t

9597 5-(31,9,3910) (complement has $\lambda=11040$)
residual design of number 9591

4508 5-(28,9,3920) (complement has $\lambda=4935$)
$Sp(6,2)$ (28 isom. types)
residual design of number 7411

10851 5-(23,12,3960) (complement has $\lambda=27864$)
supplementary design of number 10850

4072 5-(27,13,3960) (complement has $\lambda=315810$)
TvT: 5-(26,12,1440) $\cup$ 5-(26,13,2520)

8136 5-(26,10,3969) (complement has $\lambda=16380$)
derived from number 8132
design of number 8133 with respect to smaller t

8132 6-(27,11,3969) (complement has $\lambda=16380$)
design of number 8131 with respect to smaller t

548 5-(22,11,3976) (complement has $\lambda=8400$)
Alltop construction for design number 545
PGL(3,4)+ Alltop construction from 4-(21,10,3976)

7417 5-(28,9,3990) (complement has $\lambda=4865$)
residual design of number 7414

1817 5-(21,11,4004) (selfcomplementary)
supplementary design of number 1816
residual design of number 1822
residual design of complement of number 1822

512 5-(22,11,4032) (complement has $\lambda=8344$)
Alltop construction for design number 509
$PSL(3,4)+$
\cite{Kreher95}
PSL(3,4)+ Alltop construction from 4-(21,10,4032)

7843 5-(23,10,4032) (complement has $\lambda=4536$)
residual design of number 7838
design of number 7840 with respect to smaller t

2682 5-(24,11,4032) (complement has $\lambda=23100$)
\cite{Bluskov}

2718 5-(24,12,4032) (complement has $\lambda=46356$)
\cite{Bluskov}
Alltop construction for design number 2720

7396 5-(29,9,4032) (complement has $\lambda=6594$)
design of number 7395 with respect to smaller t

9349 5-(32,9,4050) (complement has $\lambda=13500$)
derived from number 9345
design of number 9346 with respect to smaller t

9345 6-(33,10,4050) (complement has $\lambda=13500$)
design of number 9344 with respect to smaller t

7925 5-(24,10,4068) (complement has $\lambda=7560$)
residual design of number 7920
derived from number 7921

7921 6-(25,11,4068) (complement has $\lambda=7560$)
residual design of number 7918

4512 5-(28,9,4095) (complement has $\lambda=4760$)
$Sp(6,2)$ (24 isom. types)
derived from number 7059
residual design of number 7424

7059 6-(29,10,4095) (complement has $\lambda=4760$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

9553 5-(33,9,4095) (complement has $\lambda=16380$)
design of number 9550 with respect to smaller t

10973 5-(23,12,4104) (complement has $\lambda=27720$)
supplementary design of number 10972

7833 5-(24,10,4104) (complement has $\lambda=7524$)
design of number 7830 with respect to smaller t
residual design of number 7889

7433 5-(28,9,4130) (complement has $\lambda=4725$)
residual design of number 7430

9368 5-(31,9,4140) (complement has $\lambda=10810$)
residual design of number 9362
derived from number 9363

9363 6-(32,10,4140) (complement has $\lambda=10810$)
residual design of number 9360

10874 5-(23,11,4158) (complement has $\lambda=14406$)
TvT: 5-(22,10,1386) $\cup$ 5-(22,11,2772)

244 5-(27,10,4158) (complement has $\lambda=22176$)
design of number 243 with respect to smaller t
TvT: 5-(26,9,945) $\cup$ 5-(26,10,3213)
derived from number 11288

11288 6-(28,11,4158) (complement has $\lambda=22176$)
TvT: 6-(27,10,945) $\cup$ 6-(27,11,3213)

7402 5-(29,9,4158) (complement has $\lambda=6468$)
design of number 7401 with respect to smaller t
derived from number 7482
residual design of number 7567

7482 6-(30,10,4158) (complement has $\lambda=6468$)
$P\Gamma L(2,27)++$ (many >= 404 isom. types) \cite{Bettenetal97b}

5379 5-(46,8,4160) (complement has $\lambda=6500$)
$M_{23}\times Id_2$

10854 5-(23,12,4176) (complement has $\lambda=27648$)
supplementary design of number 10853

8250 5-(25,10,4176) (complement has $\lambda=11328$)
residual design of number 8247
derived from number 8248

8248 6-(26,11,4176) (complement has $\lambda=11328$)
residual design of number 8246

6994 5-(28,10,4186) (complement has $\lambda=29463$)
design of number 6993 with respect to smaller t

7442 5-(28,9,4200) (complement has $\lambda=4655$)
residual design of number 7440

4808 5-(29,9,4200) (complement has $\lambda=6426$)
TvT: 5-(28,8,700) $\cup$ 5-(28,9,3500)
residual design of number 9320
derived from number 9321
design of number 10648 with respect to smaller t

9321 6-(30,10,4200) (complement has $\lambda=6426$)
residual design of number 9318
design of number 10646 with respect to smaller t

9816 5-(34,9,4200) (complement has $\lambda=19551$)
derived from number 9811

9811 6-(35,10,4200) (complement has $\lambda=19551$)
derived from number 9809

9809 7-(36,11,4200) (complement has $\lambda=19551$)
$Sp(6,2)_36$ (many isomorphism types)

10473 5-(38,9,4200) (complement has $\lambda=36720$)
residual design of number 10467
derived from number 10468

10468 6-(39,10,4200) (complement has $\lambda=36720$)
residual design of number 10465

10745 5-(24,12,4218) (complement has $\lambda=46170$)
Alltop construction for design number 10742
Tran van Trung construction with supplementary design for design number 10838

4516 5-(28,9,4235) (complement has $\lambda=4620$)
$Sp(6,2)$ (20 isom. types)

7565 5-(30,9,4250) (complement has $\lambda=8400$)
design of number 7564 with respect to smaller t
derived from number 7587

7587 6-(31,10,4250) (complement has $\lambda=8400$)
(Tran van Trung construction): 6-(30,9,680) together with 6-(30,10,3570) \cite{Bettenetal97b}

8264 5-(25,10,4272) (complement has $\lambda=11232$)
residual design of number 8258
derived from number 8259

8259 6-(26,11,4272) (complement has $\lambda=11232$)
residual design of number 8256

1857 5-(22,11,4284) (complement has $\lambda=8092$)
Tran van Trung construction with supplementary design for design number 1852
Alltop construction for design number 1854
\cite{Kreher95}
design of number 5572 with respect to smaller t
residual design of number 5607
derived from number 5608

2317 5-(23,10,4284) (selfcomplementary)
reduced 6-(23,10,1190) Halving of the complete design
design of number 5585 with respect to smaller t
complementary design of number 5585 with respect to smaller t
residual design of number 5662
residual design of complement of number 5662

2342 5-(23,11,4284) (complement has $\lambda=14280$)
TvT: 5-(22,10,1428) $\cup$ 5-(22,11,2856) \cite{TranvanTrung86}

5608 6-(23,12,4284) (complement has $\lambda=8092$)
supplementary design of number 5607
residual design of number 5612

8012 5-(26,10,4284) (complement has $\lambda=16065$)
residual design of number 8010
design of number 8011 with respect to smaller t

2675 5-(24,12,4290) (complement has $\lambda=46098$)
Alltop construction for design number 2672
\cite{Bluskov}

7067 5-(28,9,4305) (complement has $\lambda=4550$)
derived from number 7065
residual design of number 7446

7065 6-(29,10,4305) (complement has $\lambda=4550$)
$P\Gamma L(2,27)+$ \cite{Bettenetal97b}

11047 5-(23,12,4320) (complement has $\lambda=27504$)
supplementary design of number 11046

8279 5-(25,10,4320) (complement has $\lambda=11184$)
residual design of number 8276
derived from number 8277

8021 5-(25,11,4320) (complement has $\lambda=34440$)
residual design of number 8018

8277 6-(26,11,4320) (complement has $\lambda=11184$)
residual design of number 8275

9574 5-(32,9,4320) (complement has $\lambda=13230$)
residual design of number 9569
design of number 9571 with respect to smaller t

8156 5-(26,10,4347) (complement has $\lambda=16002$)
derived from number 8152
design of number 8153 with respect to smaller t

8152 6-(27,11,4347) (complement has $\lambda=16002$)
design of number 8151 with respect to smaller t

520 5-(22,11,4368) (complement has $\lambda=8008$)
Alltop construction for design number 517
PGL(3,4)+ Alltop construction from 4-(21,10,4368)

6637 5-(26,11,4368) (complement has $\lambda=49896$)
derived from number 6635

6635 6-(27,12,4368) (complement has $\lambda=49896$)
\cite{Sebille98} $AGL(3,3)$

6835 5-(27,10,4410) (complement has $\lambda=21924$)
residual design of number 6832

7454 5-(28,9,4410) (complement has $\lambda=4445$)
residual design of number 7452

7408 5-(29,9,4410) (complement has $\lambda=6216$)
design of number 7407 with respect to smaller t
derived from number 7488
residual design of number 7569

7488 6-(30,10,4410) (complement has $\lambda=6216$)
$P\Gamma L(2,27)++$ (many >= 8300 isom. types) \cite{Bettenetal97b}

8292 5-(25,10,4416) (complement has $\lambda=11088$)
residual design of number 8286
derived from number 8287

8287 6-(26,11,4416) (complement has $\lambda=11088$)
residual design of number 8284

10907 5-(24,12,4446) (complement has $\lambda=45942$)
Alltop construction for design number 10904
Tran van Trung construction with supplementary design for design number 10963

5622 5-(22,11,4452) (complement has $\lambda=7924$)
residual design of number 5618
derived from number 5619
Alltop construction for design number 5632

5619 6-(23,12,4452) (complement has $\lambda=7924$)
supplementary design of number 5618
residual design of number 5624

10877 5-(23,11,4536) (complement has $\lambda=14028$)
TvT: 5-(22,10,1512) $\cup$ 5-(22,11,3024)

10857 5-(23,12,4536) (complement has $\lambda=27288$)
supplementary design of number 10856

8672 5-(25,10,4536) (complement has $\lambda=10968$)
derived from number 8670

6373 5-(26,10,4536) (complement has $\lambda=15813$)
derived from number 6371
design of number 8172 with respect to smaller t

6334 5-(26,11,4536) (complement has $\lambda=49728$)
residual design of number 6331

8670 6-(26,11,4536) (complement has $\lambda=10968$)
derived from number 8669

6371 6-(27,11,4536) (complement has $\lambda=15813$)
\cite{Sebille98} $AGL(3,3)$
design of number 8171 with respect to smaller t

8669 7-(27,12,4536) (complement has $\lambda=10968$)
\cite{Sebille98} $AGL(3,3)$

4810 5-(29,9,4536) (complement has $\lambda=6090$)
TvT: 5-(28,8,756) $\cup$ 5-(28,9,3780)
design of number 7410 with respect to smaller t

9836 5-(34,9,4536) (complement has $\lambda=19215$)
derived from number 9831

9831 6-(35,10,4536) (complement has $\lambda=19215$)
derived from number 9829

9829 7-(36,11,4536) (complement has $\lambda=19215$)
$Sp(6,2)_36$ (many isomorphism types)

10749 5-(24,12,4560) (complement has $\lambda=45828$)
Alltop construction for design number 10746
Tran van Trung construction with supplementary design for design number 10841

11050 5-(25,11,4560) (complement has $\lambda=34200$)
TvT: 5-(24,10,1368) $\cup$ 5-(24,11,3192)

5383 5-(46,8,4580) (complement has $\lambda=6080$)
$M_{23}\times Id_2$

9594 5-(32,9,4590) (complement has $\lambda=12960$)
residual design of number 9589
design of number 9591 with respect to smaller t

9441 5-(31,9,4600) (complement has $\lambda=10350$)
residual design of number 9435

10976 5-(23,12,4608) (complement has $\lambda=27216$)
supplementary design of number 10975

7941 5-(24,10,4608) (complement has $\lambda=7020$)
residual design of number 7936
derived from number 7937

8301 5-(25,10,4608) (complement has $\lambda=10896$)
residual design of number 8299
derived from number 8300

7937 6-(25,11,4608) (complement has $\lambda=7020$)
residual design of number 7934
derived from number 10585

8300 6-(26,11,4608) (complement has $\lambda=10896$)
residual design of number 8298

10585 7-(26,12,4608) (complement has $\lambda=7020$)
derived from number 10582

10582 8-(27,13,4608) (complement has $\lambda=7020$)
$ASL(3,3)$
derived from number 10588

10588 9-(28,14,4608) (complement has $\lambda=7020$)
Alltop construction for design number 10582

2305 5-(22,11,4620) (complement has $\lambda=7756$)
$PGL(2,19)++$
Alltop construction for design number 2307

2687 5-(24,11,4620) (complement has $\lambda=22512$)
\cite{Driessen78}

540 5-(22,11,4648) (complement has $\lambda=7728$)
Alltop construction for design number 537
$PSL(3,4)+$
PGL(3,4)+ Alltop construction from 4-(21,10,4648)

9304 5-(30,9,4650) (complement has $\lambda=8000$)
derived from number 9300
design of number 9301 with respect to smaller t

9300 6-(31,10,4650) (complement has $\lambda=8000$)
design of number 9299 with respect to smaller t

8186 5-(26,10,4662) (complement has $\lambda=15687$)
derived from number 8182
design of number 8183 with respect to smaller t

8182 6-(27,11,4662) (complement has $\lambda=15687$)
design of number 8181 with respect to smaller t

7909 5-(25,10,4704) (complement has $\lambda=10800$)
derived from number 7906
design of number 7907 with respect to smaller t
residual design of number 8306

7906 6-(26,11,4704) (complement has $\lambda=10800$)
design of number 7905 with respect to smaller t
residual design of number 8305

7412 5-(29,9,4704) (complement has $\lambda=5922$)
design of number 7411 with respect to smaller t
derived from number 7494
residual design of number 7572

7494 6-(30,10,4704) (complement has $\lambda=5922$)
$P\Gamma L(2,27)++$ (many isom. types) \cite{Bettenetal97b}

5249 5-(33,9,4725) (complement has $\lambda=15750$)
TvT: 5-(32,8,675) $\cup$ 5-(32,9,4050)

8598 5-(25,11,4740) (complement has $\lambda=34020$)
residual design of number 8592
derived from number 8593

8593 6-(26,12,4740) (complement has $\lambda=34020$)
residual design of number 8590

8313 5-(25,10,4752) (complement has $\lambda=10752$)
residual design of number 8310
derived from number 8311

8311 6-(26,11,4752) (complement has $\lambda=10752$)
residual design of number 8309

1812 5-(22,11,4760) (complement has $\lambda=7616$)
Tran van Trung construction with supplementary design for design number 1809
Alltop construction for design number 1811
\cite{Kreher95}

10470 5-(39,9,4760) (complement has $\lambda=41616$)
derived from number 10466
design of number 10467 with respect to smaller t

10466 6-(40,10,4760) (complement has $\lambda=41616$)
design of number 10465 with respect to smaller t

11002 5-(24,12,4788) (complement has $\lambda=45600$)
Alltop construction for design number 10999
Tran van Trung construction with supplementary design for design number 11023

11036 5-(26,11,4788) (complement has $\lambda=49476$)
TvT: 5-(25,10,1368) $\cup$ 5-(25,11,3420)

7415 5-(29,9,4788) (complement has $\lambda=5838$)
design of number 7414 with respect to smaller t

492 5-(22,11,4816) (complement has $\lambda=7560$)
Alltop construction for design number 489
$PSL(3,4)+$
PGL(3,4)+ Alltop construction from 4-(21,10,4816)
PSL(3,4)+ Alltop construction from 4-(21,10,4816)

10860 5-(23,12,4824) (complement has $\lambda=27000$)
supplementary design of number 10859

9387 5-(31,9,4830) (complement has $\lambda=10120$)
residual design of number 9382
derived from number 9383

9383 6-(32,10,4830) (complement has $\lambda=10120$)
residual design of number 9380

8325 5-(25,10,4848) (complement has $\lambda=10656$)
residual design of number 8319
derived from number 8320

8320 6-(26,11,4848) (complement has $\lambda=10656$)
residual design of number 8317

8619 5-(25,11,4860) (complement has $\lambda=33900$)
residual design of number 8616
derived from number 8617

8617 6-(26,12,4860) (complement has $\lambda=33900$)
residual design of number 8615

9365 5-(32,9,4860) (complement has $\lambda=12690$)
derived from number 9361
design of number 9362 with respect to smaller t

9361 6-(33,10,4860) (complement has $\lambda=12690$)
design of number 9360 with respect to smaller t

2336 5-(23,12,4896) (complement has $\lambda=26928$)
supplementary design of number 2335

10753 5-(24,12,4902) (complement has $\lambda=45486$)
Alltop construction for design number 10750
Tran van Trung construction with supplementary design for design number 10844

8206 5-(26,10,4914) (complement has $\lambda=15435$)
derived from number 8202
design of number 8203 with respect to smaller t

8202 6-(27,11,4914) (complement has $\lambda=15435$)
design of number 8201 with respect to smaller t

7425 5-(29,9,4914) (complement has $\lambda=5712$)
design of number 7424 with respect to smaller t
derived from number 7500

7500 6-(30,10,4914) (complement has $\lambda=5712$)
$P\Gamma L(2,27)++$ \cite{Bettenetal97b}

9856 5-(34,9,4935) (complement has $\lambda=18816$)
derived from number 9851

9851 6-(35,10,4935) (complement has $\lambda=18816$)
derived from number 9849

9849 7-(36,11,4935) (complement has $\lambda=18816$)
$Sp(6,2)_36$ (many isomorphism types)

7568 5-(30,9,4950) (complement has $\lambda=7700$)
design of number 7567 with respect to smaller t
derived from number 7590
residual design of number 7651

7590 6-(31,10,4950) (complement has $\lambda=7700$)
(Tran van Trung construction): 6-(30,9,792) together with 6-(30,10,4158) \cite{Bettenetal97b}

2694 5-(24,11,4956) (complement has $\lambda=22176$)
\cite{Bluskov}

7431 5-(29,9,4956) (complement has $\lambda=5670$)
design of number 7430 with respect to smaller t
derived from number 7503

7503 6-(30,10,4956) (complement has $\lambda=5670$)
$P\Gamma L(2,27)++$ \cite{Bettenetal97b}

10863 5-(23,12,4968) (complement has $\lambda=26856$)
supplementary design of number 10862

484 5-(22,11,4984) (complement has $\lambda=7392$)
Alltop construction for design number 481
$PSL(3,4)+$
PSL(3,4)+ Alltop construction from 4-(21,10,4984)

9323 5-(30,9,5000) (complement has $\lambda=7650$)
derived from number 9319
design of number 9320 with respect to smaller t

9319 6-(31,10,5000) (complement has $\lambda=7650$)
design of number 9318 with respect to smaller t

2229 5-(22,11,5040) (complement has $\lambda=7336$)
Alltop construction for design number 2226
$PGL(2,19)++$

11030 5-(23,12,5040) (complement has $\lambda=26784$)
supplementary design of number 11029

8341 5-(25,10,5040) (complement has $\lambda=10464$)
residual design of number 8338
derived from number 8339

8225 5-(26,10,5040) (complement has $\lambda=15309$)
derived from number 8221
design of number 8222 with respect to smaller t

8339 6-(26,11,5040) (complement has $\lambda=10464$)
residual design of number 8337

8221 6-(27,11,5040) (complement has $\lambda=15309$)
design of number 8220 with respect to smaller t
derived from number 11332

4161 5-(28,10,5040) (complement has $\lambda=28609$)
\cite{Sebille98} $Sp(6,2)$ 129 isomorphism types

11332 7-(28,12,5040) (complement has $\lambda=15309$)
TvT: 7-(27,11,1200) $\cup$ 7-(27,12,3840)

7441 5-(29,9,5040) (complement has $\lambda=5586$)
design of number 7440 with respect to smaller t
residual design of number 7575

9572 5-(33,9,5040) (complement has $\lambda=15435$)
design of number 9569 with respect to smaller t

9876 5-(34,9,5040) (complement has $\lambda=18711$)
derived from number 9871

9871 6-(35,10,5040) (complement has $\lambda=18711$)
derived from number 9869

9869 7-(36,11,5040) (complement has $\lambda=18711$)
$Sp(6,2)_36$ (many isomorphism types)

9404 5-(31,9,5060) (complement has $\lambda=9890$)
residual design of number 9398
derived from number 9399

9399 6-(32,10,5060) (complement has $\lambda=9890$)
residual design of number 9396

10621 5-(24,10,5076) (complement has $\lambda=6552$)
derived from number 10614

10614 6-(25,11,5076) (complement has $\lambda=6552$)
derived from number 10606

10606 7-(26,12,5076) (complement has $\lambda=6552$)
derived from number 10603

10603 8-(27,13,5076) (complement has $\lambda=6552$)
$ASL(3,3)$
derived from number 10609

10609 9-(28,14,5076) (complement has $\lambda=6552$)
Alltop construction for design number 10603

7511 5-(29,9,5082) (complement has $\lambda=5544$)
derived from number 7509

7509 6-(30,10,5082) (complement has $\lambda=5544$)
$P\Gamma L(2,27)++$ \cite{Bettenetal97b}

6383 5-(26,10,5103) (complement has $\lambda=15246$)
derived from number 6381
design of number 8237 with respect to smaller t

6381 6-(27,11,5103) (complement has $\lambda=15246$)
\cite{Sebille98} $AGL(3,3)$
design of number 8236 with respect to smaller t
derived from number 8829

8829 7-(28,12,5103) (complement has $\lambda=15246$)
TvT: 7-(27,11,1215) $\cup$ 7-(27,12,3888)

2236 5-(22,11,5124) (complement has $\lambda=7252$)
Alltop construction for design number 2233
$PGL(2,19)++$

10911 5-(24,12,5130) (complement has $\lambda=45258$)
Alltop construction for design number 10908
Tran van Trung construction with supplementary design for design number 10966

8350 5-(25,10,5136) (complement has $\lambda=10368$)
residual design of number 8347
derived from number 8348

8348 6-(26,11,5136) (complement has $\lambda=10368$)
residual design of number 8346
derived from number 8681

8681 7-(27,12,5136) (complement has $\lambda=10368$)
\cite{Sebille98} $AGL(3,3)$

7956 5-(24,10,5148) (complement has $\lambda=6480$)
residual design of number 7953
derived from number 7954

7954 6-(25,11,5148) (complement has $\lambda=6480$)
residual design of number 7951
derived from number 10637

10637 7-(26,12,5148) (complement has $\lambda=6480$)
derived from number 10635

10635 8-(27,13,5148) (complement has $\lambda=6480$)
$ASL(3,3)$
derived from number 10639

10639 9-(28,14,5148) (complement has $\lambda=6480$)
Alltop construction for design number 10635

2309 5-(22,11,5152) (complement has $\lambda=7224$)
$PSL(3,4)+$
Alltop construction for design number 2311

5589 5-(23,11,5166) (complement has $\lambda=13398$)
design of number 5587 with respect to smaller t
derived from number 5592

5592 6-(24,12,5166) (complement has $\lambda=13398$)
Tran van Trung construction with supplementary design for design number 5587
design of number 5593 with respect to smaller t

7447 5-(29,9,5166) (complement has $\lambda=5460$)
design of number 7446 with respect to smaller t
derived from number 7518

7518 6-(30,10,5166) (complement has $\lambda=5460$)
$P\Gamma L(2,27)++$ \cite{Bettenetal97b}

10866 5-(23,12,5184) (complement has $\lambda=26640$)
supplementary design of number 10865

10491 5-(24,10,5184) (complement has $\lambda=6444$)
residual design of number 10489
derived from number 10490

8358 5-(25,10,5184) (complement has $\lambda=10320$)
residual design of number 8356
derived from number 8357
design of number 10501 with respect to smaller t

10490 6-(25,11,5184) (complement has $\lambda=6444$)
residual design of number 10487

8357 6-(26,11,5184) (complement has $\lambda=10320$)
residual design of number 8355
derived from number 8687
design of number 10499 with respect to smaller t

8687 7-(27,12,5184) (complement has $\lambda=10320$)
\cite{Sebille98} $AGL(3,3)$
design of number 10498 with respect to smaller t

536 5-(22,11,5208) (complement has $\lambda=7168$)
Alltop construction for design number 533
PGL(3,4)+ Alltop construction from 4-(21,10,5208)

1866 5-(22,11,5236) (complement has $\lambda=7140$)
Tran van Trung construction with supplementary design for design number 1861
Alltop construction for design number 1863
\cite{Kreher95}
design of number 5573 with respect to smaller t

7570 5-(30,9,5250) (complement has $\lambda=7400$)
design of number 7569 with respect to smaller t
derived from number 7592

7592 6-(31,10,5250) (complement has $\lambda=7400$)
(Tran van Trung construction): 6-(30,9,840) together with 6-(30,10,4410) \cite{Bettenetal97b}

10979 5-(23,12,5256) (complement has $\lambda=26568$)
supplementary design of number 10978

9896 5-(34,9,5271) (complement has $\lambda=18480$)
derived from number 9891

9891 6-(35,10,5271) (complement has $\lambda=18480$)
derived from number 9889

9889 7-(36,11,5271) (complement has $\lambda=18480$)
$Sp(6,2)_36$ (many isomorphism types)

8370 5-(25,10,5280) (complement has $\lambda=10224$)
residual design of number 8364
derived from number 8365

8365 6-(26,11,5280) (complement has $\lambda=10224$)
residual design of number 8362

5159 5-(31,9,5280) (complement has $\lambda=9670$)
derived from number 5157

5157 6-(32,10,5280) (complement has $\lambda=9670$)
$AGL(4,2)\times C_2$

7453 5-(29,9,5292) (complement has $\lambda=5334$)
design of number 7452 with respect to smaller t
derived from number 7521
residual design of number 7552

7521 6-(30,10,5292) (complement has $\lambda=5334$)
$P\Gamma L(2,27)++$ (>= 4970 isom. types) \cite{Bettenetal97b}

2532 5-(24,10,5310) (complement has $\lambda=6318$)
$PSL(2,23)$ (many isomorphism types)

11356 5-(28,10,5313) (complement has $\lambda=28336$)
TvT: 5-(27,9,1155) $\cup$ 5-(27,10,4158)

9592 5-(33,9,5355) (complement has $\lambda=15120$)
design of number 9589 with respect to smaller t

500 5-(22,11,5376) (complement has $\lambda=7000$)
Alltop construction for design number 497
$PSL(3,4)+$
PSL(3,4)+ Alltop construction from 4-(21,10,5376)

9916 5-(34,9,5376) (complement has $\lambda=18375$)
derived from number 9911

9911 6-(35,10,5376) (complement has $\lambda=18375$)
derived from number 9909

9909 7-(36,11,5376) (complement has $\lambda=18375$)
$Sp(6,2)_36$ (many isomorphism types)

4824 5-(30,14,5390) (complement has $\lambda=2037585$)
\cite{MacWilliamsetal78}

10869 5-(23,12,5400) (complement has $\lambda=26424$)
supplementary design of number 10868

2540 5-(24,10,5400) (complement has $\lambda=6228$)
$PSL(2,23)$ (many isomorphism types)

8034 5-(25,11,5400) (complement has $\lambda=33360$)
residual design of number 8028

9438 5-(32,9,5400) (complement has $\lambda=12150$)
residual design of number 9433
design of number 9435 with respect to smaller t

5595 5-(22,12,5412) (complement has $\lambda=14036$)
residual design of number 5588

7923 5-(25,10,5424) (complement has $\lambda=10080$)
derived from number 7919
design of number 7920 with respect to smaller t

7919 6-(26,11,5424) (complement has $\lambda=10080$)
design of number 7918 with respect to smaller t

2242 5-(22,11,5460) (complement has $\lambda=6916$)
Alltop construction for design number 2239

7841 5-(24,10,5472) (complement has $\lambda=6156$)
design of number 7838 with respect to smaller t
residual design of number 7892

2331 5-(24,12,5472) (complement has $\lambda=44916$)
Tran van Trung construction with supplementary design for design number 2328
Alltop construction for design number 2330

7890 5-(25,10,5472) (complement has $\lambda=10032$)
design of number 7889 with respect to smaller t
residual design of number 7902
derived from number 8377

8377 6-(26,11,5472) (complement has $\lambda=10032$)
residual design of number 8376

6392 5-(26,10,5481) (complement has $\lambda=14868$)
derived from number 6390
design of number 8247 with respect to smaller t

6390 6-(27,11,5481) (complement has $\lambda=14868$)
\cite{Sebille98} $AGL(3,3)$
design of number 8246 with respect to smaller t

5272 5-(34,9,5481) (complement has $\lambda=18270$)
TvT: 5-(33,8,756) $\cup$ 5-(33,9,4725)

9468 5-(31,9,5520) (complement has $\lambda=9430$)
residual design of number 9462

2544 5-(24,10,5526) (complement has $\lambda=6102$)
$PSL(2,23)$ (many isomorphism types)

488 5-(22,11,5544) (complement has $\lambda=6832$)
Alltop construction for design number 485
$PSL(3,4)+$ Alltop construction from 4-(21,10,5544)

2548 5-(24,10,5544) (complement has $\lambda=6084$)
$PSL(2,23)$ (many isomorphism types)

6344 5-(26,11,5544) (complement has $\lambda=48720$)
residual design of number 6341

4190 5-(27,10,5544) (complement has $\lambda=20790$)
residual design of number 4189
design of number 8010 with respect to smaller t

2552 5-(24,10,5562) (complement has $\lambda=6066$)
$PSL(2,23)$ (many isomorphism types)

8382 5-(25,10,5568) (complement has $\lambda=9936$)
residual design of number 8379
derived from number 8380

8380 6-(26,11,5568) (complement has $\lambda=9936$)
residual design of number 8378

10915 5-(24,12,5586) (complement has $\lambda=44802$)
Alltop construction for design number 10912
Tran van Trung construction with supplementary design for design number 10969

2560 5-(24,10,5598) (complement has $\lambda=6030$)
$PSL(2,23)$ (many isomorphism types)

7573 5-(30,9,5600) (complement has $\lambda=7050$)
design of number 7572 with respect to smaller t
derived from number 7595

7595 6-(31,10,5600) (complement has $\lambda=7050$)
(Tran van Trung construction): 6-(30,9,896) together with 6-(30,10,4704) \cite{Bettenetal97b}

8261 5-(26,10,5607) (complement has $\lambda=14742$)
derived from number 8257
design of number 8258 with respect to smaller t

8257 6-(27,11,5607) (complement has $\lambda=14742$)
design of number 8256 with respect to smaller t

8396 5-(25,10,5616) (complement has $\lambda=9888$)
residual design of number 8390
derived from number 8391

8391 6-(26,11,5616) (complement has $\lambda=9888$)
residual design of number 8388

6833 5-(28,10,5635) (complement has $\lambda=28014$)
design of number 6832 with respect to smaller t

2564 5-(24,10,5652) (complement has $\lambda=5976$)
$PSL(2,23)$ (many isomorphism types)

544 5-(22,11,5656) (complement has $\lambda=6720$)
Alltop construction for design number 541
\cite{Kreher95}
$PGL(3,4)+$ Alltop construction from 4-(21,10,5656)

10880 5-(23,11,5670) (complement has $\lambda=12894$)
TvT: 5-(22,10,1890) $\cup$ 5-(22,11,3780)

6402 5-(26,10,5670) (complement has $\lambda=14679$)
derived from number 6400
design of number 8276 with respect to smaller t

6400 6-(27,11,5670) (complement has $\lambda=14679$)
\cite{Sebille98} $AGL(3,3)$
design of number 8275 with respect to smaller t

9384 5-(32,9,5670) (complement has $\lambda=11880$)
derived from number 9381
design of number 9382 with respect to smaller t
residual design of number 9453

9381 6-(33,10,5670) (complement has $\lambda=11880$)
design of number 9380 with respect to smaller t
residual design of number 9608

7962 5-(24,10,5688) (complement has $\lambda=5940$)
residual design of number 7959
derived from number 7960

7960 6-(25,11,5688) (complement has $\lambda=5940$)
residual design of number 7957

1873 5-(22,11,5712) (complement has $\lambda=6664$)
Tran van Trung construction with supplementary design for design number 1870
Alltop construction for design number 1872
\cite{Kreher95} $PSL(3,4)+$
design of number 5574 with respect to smaller t
residual design of number 11500
derived from number 11501

2349 5-(23,11,5712) (complement has $\lambda=12852$)
TvT: 5-(22,10,1904) $\cup$ 5-(22,11,3808)

11501 6-(23,12,5712) (complement has $\lambda=6664$)
supplementary design of number 11500
residual design of number 11503

8410 5-(25,10,5712) (complement has $\lambda=9792$)
residual design of number 8408
derived from number 8409

8409 6-(26,11,5712) (complement has $\lambda=9792$)
residual design of number 8407

2568 5-(24,10,5724) (complement has $\lambda=5904$)
$PSL(2,23)$ (many isomorphism types)

9484 5-(31,9,5750) (complement has $\lambda=9200$)
residual design of number 9481

2576 5-(24,10,5760) (complement has $\lambda=5868$)
$PSL(2,23)$ (many isomorphism types)

9936 5-(34,9,5775) (complement has $\lambda=17976$)
derived from number 9931

9931 6-(35,10,5775) (complement has $\lambda=17976$)
derived from number 9929

9929 7-(36,11,5775) (complement has $\lambda=17976$)
$Sp(6,2)_36$ (many isomorphism types)

7970 5-(24,10,5778) (complement has $\lambda=5850$)
residual design of number 7965
derived from number 7966

7966 6-(25,11,5778) (complement has $\lambda=5850$)
residual design of number 7963

2254 5-(22,11,5796) (complement has $\lambda=6580$)
Alltop construction for design number 2251

7984 5-(24,10,5796) (complement has $\lambda=5832$)
derived from number 7980
residual design of number 10517

7980 6-(25,11,5796) (complement has $\lambda=5832$)
derived from number 7978
residual design of number 10516

8289 5-(26,10,5796) (complement has $\lambda=14553$)
derived from number 8285
design of number 8286 with respect to smaller t

7978 7-(26,12,5796) (complement has $\lambda=5832$)
$P\Gamma L(2,25)$(>=1 isom. type)
residual design of number 10515

8285 6-(27,11,5796) (complement has $\lambda=14553$)
design of number 8284 with respect to smaller t

2580 5-(24,10,5814) (selfcomplementary)
$PSL(2,23)$ (many isomorphism types) halving of complete design!
design of number 5662 with respect to smaller t
complementary design of number 5662 with respect to smaller t
residual design of number 5788
residual design of complement of number 5788

2260 5-(22,11,5824) (complement has $\lambda=6552$)
Alltop construction for design number 2257
$PSL(3,4)+$

8700 5-(25,10,5832) (complement has $\lambda=9672$)
derived from number 8695

8695 6-(26,11,5832) (complement has $\lambda=9672$)
derived from number 8693

8693 7-(27,12,5832) (complement has $\lambda=9672$)
$ASL(3,3)$

5015 5-(31,9,5850) (complement has $\lambda=9100$)
TvT: 5-(30,8,900) $\cup$ 5-(30,9,4950)
design of number 7651 with respect to smaller t
derived from number 7652

7652 6-(32,10,5850) (complement has $\lambda=9100$)
TvT: 6-(31,9,900) $\cup$ 6-(31,10,4950)

528 5-(22,11,5880) (complement has $\lambda=6496$)
Alltop construction for design number 525
$PGL(3,4)+$, $PGL(2,19)++$, Alltop construction from 4-(21,10,5880)

9956 5-(34,9,5880) (complement has $\lambda=17871$)
derived from number 9951

9951 6-(35,10,5880) (complement has $\lambda=17871$)
derived from number 9949

9949 7-(36,11,5880) (complement has $\lambda=17871$)
$Sp(6,2)_36$ (many isomorphism types)

8418 5-(25,10,5904) (complement has $\lambda=9600$)
residual design of number 8415
derived from number 8416

8416 6-(26,11,5904) (complement has $\lambda=9600$)
residual design of number 8414

10757 5-(24,12,5928) (complement has $\lambda=44460$)
Alltop construction for design number 10754
Tran van Trung construction with supplementary design for design number 10847

9401 5-(32,9,5940) (complement has $\lambda=11610$)
derived from number 9397
design of number 9398 with respect to smaller t

9397 6-(33,10,5940) (complement has $\lambda=11610$)
design of number 9396 with respect to smaller t

5642 5-(22,11,5964) (complement has $\lambda=6412$)
residual design of number 5638
derived from number 5639
Alltop construction for design number 5652

5639 6-(23,12,5964) (complement has $\lambda=6412$)
supplementary design of number 5638
residual design of number 5644

2313 5-(22,11,5992) (complement has $\lambda=6384$)
$PSL(3,4)+$
Alltop construction for design number 2315

8431 5-(25,10,6000) (complement has $\lambda=9504$)
residual design of number 8425
derived from number 8426

8426 6-(26,11,6000) (complement has $\lambda=9504$)
residual design of number 8423

7576 5-(30,9,6000) (complement has $\lambda=6650$)
design of number 7575 with respect to smaller t

5666 5-(23,11,6006) (complement has $\lambda=12558$)
residual design of number 5663

496 5-(22,11,6048) (complement has $\lambda=6328$)
Alltop construction for design number 493
$PSL(3,4)+$ Alltop construction from 4-(21,10,6048)

8445 5-(25,10,6048) (complement has $\lambda=9456$)
residual design of number 8439
derived from number 8440

6410 5-(26,10,6048) (complement has $\lambda=14301$)
derived from number 6408
design of number 8299 with respect to smaller t

6354 5-(26,11,6048) (complement has $\lambda=48216$)
residual design of number 6351
design of number 8018 with respect to smaller t

8440 6-(26,11,6048) (complement has $\lambda=9456$)
residual design of number 8437

6408 6-(27,11,6048) (complement has $\lambda=14301$)
\cite{Sebille98} $AGL(3,3)$
design of number 8298 with respect to smaller t

7460 5-(29,10,6048) (complement has $\lambda=36456$)
residual design of number 7458

4314 5-(28,13,6072) (complement has $\lambda=484242$)
TvT: 5-(27,12,2112) $\cup$ 5-(27,13,3960)

9976 5-(34,9,6111) (complement has $\lambda=17640$)
derived from number 9971

9971 6-(35,10,6111) (complement has $\lambda=17640$)
derived from number 9969

9969 7-(36,11,6111) (complement has $\lambda=17640$)
$Sp(6,2)_36$ (many isomorphism types)

11485 5-(23,12,6120) (complement has $\lambda=25704$)
supplementary design of number 11484
design of number 11495 with respect to smaller t
residual design of number 11496

8052 5-(25,11,6120) (complement has $\lambda=32640$)
residual design of number 8048

7938 5-(25,10,6144) (complement has $\lambda=9360$)
derived from number 7935
design of number 7936 with respect to smaller t
residual design of number 8458

7935 6-(26,11,6144) (complement has $\lambda=9360$)
design of number 7934 with respect to smaller t
residual design of number 8457
derived from number 11560

11560 7-(27,12,6144) (complement has $\lambda=9360$)
TvT: 7-(26,11,1536) $\cup$ 7-(26,12,4608)

11006 5-(24,12,6156) (complement has $\lambda=44232$)
Alltop construction for design number 11003
Tran van Trung construction with supplementary design for design number 11026

4073 5-(27,14,6160) (complement has $\lambda=491260$)
supplementary design of number 4072

6419 5-(26,10,6174) (complement has $\lambda=14175$)
derived from number 6417
design of number 8306 with respect to smaller t

6417 6-(27,11,6174) (complement has $\lambda=14175$)
\cite{Sebille98} $AGL(3,3)$
design of number 8305 with respect to smaller t

1821 5-(22,11,6188) (selfcomplementary)
Tran van Trung construction with supplementary design for design number 1816
Alltop construction for design number 1818
design of number 1822 with respect to smaller t
complementary design of number 1822 with respect to smaller t

9996 5-(34,9,6216) (complement has $\lambda=17535$)
derived from number 9991

9991 6-(35,10,6216) (complement has $\lambda=17535$)
derived from number 9989

9989 7-(36,11,6216) (complement has $\lambda=17535$)
$Sp(6,2)_36$ (many isomorphism types)

6427 5-(26,10,6237) (complement has $\lambda=14112$)
derived from number 6425
design of number 8310 with respect to smaller t

6332 5-(27,11,6237) (complement has $\lambda=68376$)
design of number 6331 with respect to smaller t

6425 6-(27,11,6237) (complement has $\lambda=14112$)
\cite{Sebille98} $AGL(3,3)$
design of number 8309 with respect to smaller t

5169 5-(31,9,6240) (complement has $\lambda=8710$)
derived from number 5167

5167 6-(32,10,6240) (complement has $\lambda=8710$)
$AGL(4,2)\times C_2$

10761 5-(24,12,6270) (complement has $\lambda=44118$)
Alltop construction for design number 10758
Tran van Trung construction with supplementary design for design number 10850

7553 5-(30,9,6300) (complement has $\lambda=6350$)
design of number 7552 with respect to smaller t
derived from number 7598

7598 6-(31,10,6300) (complement has $\lambda=6350$)
(Tran van Trung construction): 6-(30,9,1008) together with 6-(30,10,5292) \cite{Bettenetal97b}

9436 5-(33,9,6300) (complement has $\lambda=14175$)
design of number 9433 with respect to smaller t

2730 5-(24,12,6336) (complement has $\lambda=44052$)
Alltop construction for design number 2732

8465 5-(25,10,6336) (complement has $\lambda=9168$)
residual design of number 8462
derived from number 8463

8463 6-(26,11,6336) (complement has $\lambda=9168$)
residual design of number 8461

8631 5-(25,11,6360) (complement has $\lambda=32400$)
residual design of number 8628
derived from number 8629

8629 6-(26,12,6360) (complement has $\lambda=32400$)
residual design of number 8627

8322 5-(26,10,6363) (complement has $\lambda=13986$)
derived from number 8318
design of number 8319 with respect to smaller t

8318 6-(27,11,6363) (complement has $\lambda=13986$)
design of number 8317 with respect to smaller t

2734 5-(24,12,6384) (complement has $\lambda=44004$)
Alltop construction for design number 2736

11051 5-(26,11,6384) (complement has $\lambda=47880$)
TvT: 5-(25,10,1824) $\cup$ 5-(25,11,4560)

5179 5-(31,9,6390) (complement has $\lambda=8560$)
derived from number 5177

5177 6-(32,10,6390) (complement has $\lambda=8560$)
$AGL(4,2)\times C_2$

5609 5-(23,11,6426) (complement has $\lambda=12138$)
design of number 5607 with respect to smaller t
derived from number 5611

5611 6-(24,12,6426) (complement has $\lambda=12138$)
Tran van Trung construction with supplementary design for design number 5607
design of number 5612 with respect to smaller t

8477 5-(25,10,6432) (complement has $\lambda=9072$)
residual design of number 8471
derived from number 8472

8472 6-(26,11,6432) (complement has $\lambda=9072$)
residual design of number 8469
derived from number 8718

8718 7-(27,12,6432) (complement has $\lambda=9072$)
\cite{Sebille98} $AGL(3,3)$

9498 5-(31,9,6440) (complement has $\lambda=8510$)
residual design of number 9492

10872 5-(23,12,6480) (complement has $\lambda=25344$)
supplementary design of number 10871

8491 5-(25,10,6480) (complement has $\lambda=9024$)
residual design of number 8488
derived from number 8489

8065 5-(25,11,6480) (complement has $\lambda=32280$)
residual design of number 8060
derived from number 8640

8489 6-(26,11,6480) (complement has $\lambda=9024$)
residual design of number 8487
derived from number 8729

8640 6-(26,12,6480) (complement has $\lambda=32280$)
residual design of number 8639

8729 7-(27,12,6480) (complement has $\lambda=9024$)
\cite{Sebille98} $AGL(3,3)$ many isomorphism types

9465 5-(32,9,6480) (complement has $\lambda=11070$)
residual design of number 9460
design of number 9462 with respect to smaller t

10919 5-(24,12,6498) (complement has $\lambda=43890$)
Alltop construction for design number 10916
Tran van Trung construction with supplementary design for design number 10972

5680 5-(23,11,6510) (complement has $\lambda=12054$)
derived from number 5678

5678 6-(24,12,6510) (complement has $\lambda=12054$)
PSL(2,23) (>=2 isom. types)

2356 5-(23,11,6552) (complement has $\lambda=12012$)
TvT: 5-(22,10,2184) $\cup$ 5-(22,11,4368)

8500 5-(25,10,6576) (complement has $\lambda=8928$)
residual design of number 8497
derived from number 8498

8498 6-(26,11,6576) (complement has $\lambda=8928$)
residual design of number 8496

3833 5-(25,12,6600) (complement has $\lambda=70920$)
TvT: 5-(24,11,2310) $\cup$ 5-(24,12,4290)

10765 5-(24,12,6612) (complement has $\lambda=43776$)
Alltop construction for design number 10762
Tran van Trung construction with supplementary design for design number 10853

6435 5-(26,10,6615) (complement has $\lambda=13734$)
derived from number 6433
design of number 8338 with respect to smaller t

6433 6-(27,11,6615) (complement has $\lambda=13734$)
\cite{Sebille98} $AGL(3,3)$
design of number 8337 with respect to smaller t

4197 5-(33,9,6615) (complement has $\lambda=13860$)
derived from number 4195
design of number 9453 with respect to smaller t

10016 5-(34,9,6615) (complement has $\lambda=17136$)
derived from number 10011

4195 6-(34,10,6615) (complement has $\lambda=13860$)
\cite{Sebille98} $P\Gamma L(2,32)\cup S_2$
\cite{Sebille98} $P\Gamma L(2,32)\cup S_2$
TvT: 6-(33,9,945) $\cup$ 6-(33,10,5670)
design of number 9608 with respect to smaller t

10011 6-(35,10,6615) (complement has $\lambda=17136$)
derived from number 10009

10009 7-(36,11,6615) (complement has $\lambda=17136$)
$Sp(6,2)_36$ (many isomorphism types)

8595 5-(26,11,6636) (complement has $\lambda=47628$)
derived from number 8591
design of number 8592 with respect to smaller t

8591 6-(27,12,6636) (complement has $\lambda=47628$)
design of number 8590 with respect to smaller t

9518 5-(31,9,6670) (complement has $\lambda=8280$)
residual design of number 9512

5620 5-(23,11,6678) (complement has $\lambda=11886$)
design of number 5618 with respect to smaller t
derived from number 5623

5623 6-(24,12,6678) (complement has $\lambda=11886$)
Tran van Trung construction with supplementary design for design number 5618
design of number 5624 with respect to smaller t

10982 5-(23,12,6696) (complement has $\lambda=25128$)
supplementary design of number 10981

8082 5-(25,11,6720) (complement has $\lambda=32040$)
residual design of number 8076

4165 5-(28,10,6720) (complement has $\lambda=26929$)
\cite{Sebille98} $Sp(6,2)$ 412 isomorphism types

10036 5-(34,9,6720) (complement has $\lambda=17031$)
derived from number 10031

10031 6-(35,10,6720) (complement has $\lambda=17031$)
derived from number 10029

10029 7-(36,11,6720) (complement has $\lambda=17031$)
$Sp(6,2)_36$ (many isomorphism types)

5614 5-(22,12,6732) (complement has $\lambda=12716$)
residual design of number 5608

6444 5-(26,10,6741) (complement has $\lambda=13608$)
derived from number 6442
design of number 8347 with respect to smaller t

6442 6-(27,11,6741) (complement has $\lambda=13608$)
\cite{Sebille98} $AGL(3,3)$
design of number 8346 with respect to smaller t
derived from number 8830

8830 7-(28,12,6741) (complement has $\lambda=13608$)
TvT: 7-(27,11,1605) $\cup$ 7-(27,12,5136)

9483 5-(32,9,6750) (complement has $\lambda=10800$)
residual design of number 9480
design of number 9481 with respect to smaller t

8514 5-(25,10,6768) (complement has $\lambda=8736$)
residual design of number 8508
derived from number 8509

8509 6-(26,11,6768) (complement has $\lambda=8736$)
residual design of number 8506

6453 5-(26,10,6804) (complement has $\lambda=13545$)
derived from number 6451
design of number 8356 with respect to smaller t

6646 5-(26,11,6804) (complement has $\lambda=47460$)
derived from number 6644
design of number 8616 with respect to smaller t

6845 5-(27,10,6804) (complement has $\lambda=19530$)
residual design of number 6842

6451 6-(27,11,6804) (complement has $\lambda=13545$)
\cite{Sebille98} $AGL(3,3)$
design of number 8355 with respect to smaller t
derived from number 8831

6644 6-(27,12,6804) (complement has $\lambda=47460$)
\cite{Sebille98} $AGL(3,3)$
design of number 8615 with respect to smaller t

8831 7-(28,12,6804) (complement has $\lambda=13545$)
TvT: 7-(27,11,1620) $\cup$ 7-(27,12,5184)

11044 5-(24,12,6840) (complement has $\lambda=43548$)
Alltop construction for design number 11041
Tran van Trung construction with supplementary design for design number 11046

11090 5-(25,12,6840) (complement has $\lambda=70680$)
TvT: 5-(24,11,2394) $\cup$ 5-(24,12,4446)

7955 5-(25,10,6864) (complement has $\lambda=8640$)
derived from number 7952
design of number 7953 with respect to smaller t
residual design of number 8526

7952 6-(26,11,6864) (complement has $\lambda=8640$)
design of number 7951 with respect to smaller t
residual design of number 8525
derived from number 11549

11549 7-(27,12,6864) (complement has $\lambda=8640$)
TvT: 7-(26,11,1716) $\cup$ 7-(26,12,5148)

5189 5-(31,9,6870) (complement has $\lambda=8080$)
derived from number 5187

5187 6-(32,10,6870) (complement has $\lambda=8080$)
$AGL(4,2)\times C_2$

2738 5-(24,12,6912) (complement has $\lambda=43476$)
Alltop construction for design number 2740

8532 5-(25,10,6912) (complement has $\lambda=8592$)
residual design of number 8530
derived from