# 6800: 5-(24,9,1782)

- clan: 11-(30,15,1782), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1782), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1782) (# 6800) : der= 5-(24,9,1782) and res= 5-(24,10,5346) - the given design is the derived.
- derived from 6-(26,11,7128) (# 14852)
- derived from supplementary of 6-(26,11,8376) (# 14855)

- clan: 13-(32,16,447), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,447), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1788) (# 6802) : der= 5-(24,8,447) and res= 5-(24,9,1788) - the given design is the residual.

- clan: 13-(32,16,447), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1788) (# 6802) : der= 5-(24,9,1788) and res= 5-(24,10,5364) - the given design is the derived.

- clan: 13-(32,16,447), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2235) (# 6803) : der= 5-(25,9,2235) and res= 5-(25,10,7152) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7152) (# 6804) : der= 5-(25,9,2235) and res= 5-(25,10,7152) - the given design is the residual.

- clan: 11-(30,15,1794), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1794), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1794) (# 6806) : der= 5-(24,9,1794) and res= 5-(24,10,5382) - the given design is the derived.

- clan: 13-(32,16,45), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,45), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,180) (# 6808) : der= 5-(24,8,45) and res= 5-(24,9,180) - the given design is the residual.

- clan: 13-(32,16,45), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,180) (# 6808) : der= 5-(24,9,180) and res= 5-(24,10,540) - the given design is the derived.

- clan: 13-(32,16,45), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,225) (# 6809) : der= 5-(25,9,225) and res= 5-(25,10,720) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,720) (# 6810) : der= 5-(25,9,225) and res= 5-(25,10,720) - the given design is the residual.

- clan: 13-(32,16,45), 2 times reduced t, 5 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(25,10,720) (# 6810) : der= 5-(25,10,720) and res= 5-(25,11,1800) - the given design is the derived.

- clan: 13-(32,16,45), 3 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(26,10,945) (# 6811) : der= 5-(26,10,945) and res= 5-(26,11,2520) - the given design is the derived.
- Tran van Trung construction (left) for 5-(26,11,2520) (# 6812) : der= 5-(26,10,945) and res= 5-(26,11,2520) - the given design is the residual.

- clan: 13-(32,16,45), 3 times reduced t, 4 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(26,11,2520) (# 6812) : der= 5-(26,11,2520) and res= 5-(26,12,5400) - the given design is the derived.

- clan: 13-(32,16,45), 4 times reduced t, 4 times derived
- Tran van Trung construction (right) for 5-(27,11,3465) (# 6813) : der= 5-(27,11,3465) and res= 5-(27,12,7920) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,12,7920) (# 6814) : der= 5-(27,11,3465) and res= 5-(27,12,7920) - the given design is the residual.

- clan: 13-(32,16,45), 4 times reduced t, 3 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(27,12,7920) (# 6814) : der= 5-(27,12,7920) and res= 5-(27,13,14850) - the given design is the derived.

- clan: 13-(32,16,45), 5 times reduced t, 3 times derived
- Tran van Trung construction (right) for 5-(28,12,11385) (# 6815) : der= 5-(28,12,11385) and res= 5-(28,13,22770) - the given design is the derived.
- Tran van Trung construction (left) for 5-(28,13,22770) (# 6816) : der= 5-(28,12,11385) and res= 5-(28,13,22770) - the given design is the residual.

- clan: 13-(32,16,45), 5 times reduced t, 2 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(28,13,22770) (# 6816) : der= 5-(28,13,22770) and res= 5-(28,14,37950) - the given design is the derived.

- clan: 13-(32,16,45), 6 times reduced t, 2 times derived
- Tran van Trung construction (right) for 5-(29,13,34155) (# 6817) : der= 5-(29,13,34155) and res= 5-(29,14,60720) - the given design is the derived.
- Tran van Trung construction (left) for 5-(29,14,60720) (# 6818) : der= 5-(29,13,34155) and res= 5-(29,14,60720) - the given design is the residual.

- clan: 13-(32,16,45), 6 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction with complementary design for 5-(29,14,60720) (# 6818)

- clan: 13-(32,16,45), 7 times reduced t, 1 times derived
- Tran van Trung construction (right) for 5-(30,14,94875) (# 6819) : der= 5-(30,14,94875) and res= 5-(30,15,151800) - the given design is the derived.
- Tran van Trung construction (left) for 5-(30,15,151800) (# 6820) : der= 5-(30,14,94875) and res= 5-(30,15,151800) - the given design is the residual.

- clan: 13-(32,16,45), 8 times reduced t
- Tran van Trung construction with complementary design for 5-(31,15,246675) (# 6821)

- clan: 13-(32,16,450), 7 times derived, 1 times residual
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 13-(32,16,450), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1800) (# 6823) : der= 5-(24,8,450) and res= 5-(24,9,1800) - the given design is the residual.
- derived from 6-(26,10,2250) (# 14283)
- derived from supplementary of 6-(26,10,2595) (# 14286)

- clan: 13-(32,16,450), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1800) (# 6823) : der= 5-(24,9,1800) and res= 5-(24,10,5400) - the given design is the derived.
- residual design of 6-(26,10,2250) (# 14283)
- derived from 6-(26,11,7200) (# 14284)
- residual design of supplementary of 6-(26,10,2595) (# 14286)
- derived from supplementary of 6-(26,11,8304) (# 14287)

- clan: 13-(32,16,450), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2250) (# 6824) : der= 5-(25,9,2250) and res= 5-(25,10,7200) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7200) (# 6825) : der= 5-(25,9,2250) and res= 5-(25,10,7200) - the given design is the residual.
- derived from 6-(27,11,9450) (# 14282)
- design 6-(26,10,2250) (# 14283) with respect to smaller t
- derived from supplementary of 6-(27,11,10899) (# 14285)
- supplementary design of 6-(26,10,2595) (# 14286) with respect to smaller t

- clan: 11-(30,15,1806), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,1806), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1806) (# 6827) : der= 5-(24,9,1806) and res= 5-(24,10,5418) - the given design is the derived.

- clan: 13-(32,16,453), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,453), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1812) (# 6829) : der= 5-(24,8,453) and res= 5-(24,9,1812) - the given design is the residual.

- clan: 13-(32,16,453), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1812) (# 6829) : der= 5-(24,9,1812) and res= 5-(24,10,5436) - the given design is the derived.

- clan: 13-(32,16,453), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2265) (# 6830) : der= 5-(25,9,2265) and res= 5-(25,10,7248) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7248) (# 6831) : der= 5-(25,9,2265) and res= 5-(25,10,7248) - the given design is the residual.

- clan: 11-(30,15,1818), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1818), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1818) (# 6833) : der= 5-(24,9,1818) and res= 5-(24,10,5454) - the given design is the derived.

- clan: 15-(32,16,8), 2 times reduced t, 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)
- Tran van Trung construction (right) for 5-(23,8,384) (# 9853) : der= 5-(23,8,384) and res= 5-(23,9,1440) - the given design is the derived.
- design 6-(24,9,384) (# 13389) with respect to smaller t
- supplementary design of 6-(24,9,432) (# 13390) with respect to smaller t
- residual design of 6-(25,9,456) (# 13391)
- derived from 6-(25,10,1824) (# 13392)
- residual design of supplementary of 6-(25,9,513) (# 13393)
- derived from supplementary of 6-(25,10,2052) (# 13394)

- clan: 15-(32,16,8), 3 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1824) (# 6835) : der= 5-(24,8,456) and res= 5-(24,9,1824) - the given design is the residual.
- design 6-(25,9,456) (# 13391) with respect to smaller t
- supplementary design of 6-(25,9,513) (# 13393) with respect to smaller t
- derived from 6-(26,10,2280) (# 13395)
- derived from supplementary of 6-(26,10,2565) (# 13397)

- clan: 15-(32,16,8), 3 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1824) (# 6835) : der= 5-(24,9,1824) and res= 5-(24,10,5472) - the given design is the derived.
- design 6-(25,10,1824) (# 13392) with respect to smaller t
- supplementary design of 6-(25,10,2052) (# 13394) with respect to smaller t
- residual design of 6-(26,10,2280) (# 13395)
- derived from 6-(26,11,7296) (# 13396)
- residual design of supplementary of 6-(26,10,2565) (# 13397)
- derived from supplementary of 6-(26,11,8208) (# 13398)

- clan: 15-(32,16,8), 4 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2280) (# 6836) : der= 5-(25,9,2280) and res= 5-(25,10,7296) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7296) (# 6837) : der= 5-(25,9,2280) and res= 5-(25,10,7296) - the given design is the residual.
- derived from 6-(27,11,9576) (# 10755)
- design 6-(26,10,2280) (# 13395) with respect to smaller t
- supplementary design of 6-(26,10,2565) (# 13397) with respect to smaller t
- derived from supplementary of 6-(27,11,10773) (# 13400)

- clan: 15-(32,16,8), 4 times reduced t, 5 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(25,10,7296) (# 6837) : der= 5-(25,10,7296) and res= 5-(25,11,18240) - the given design is the derived.
- residual design of 6-(27,11,9576) (# 10755)
- design 6-(26,11,7296) (# 13396) with respect to smaller t
- supplementary design of 6-(26,11,8208) (# 13398) with respect to smaller t
- derived from 6-(27,12,25536) (# 13399)
- residual design of supplementary of 6-(27,11,10773) (# 13400)
- derived from supplementary of 6-(27,12,28728) (# 13401)

- clan: 15-(32,16,8), 5 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(26,10,9576) (# 6838) : der= 5-(26,10,9576) and res= 5-(26,11,25536) - the given design is the derived.
- Tran van Trung construction (left) for 5-(26,11,25536) (# 6839) : der= 5-(26,10,9576) and res= 5-(26,11,25536) - the given design is the residual.
- design 6-(27,11,9576) (# 10755) with respect to smaller t
- supplementary design of 6-(27,11,10773) (# 13400) with respect to smaller t
- derived from 6-(28,12,35112) (# 13402)
- derived from supplementary of 6-(28,12,39501) (# 13404)

- clan: 15-(32,16,8), 5 times reduced t, 4 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(26,11,25536) (# 6839) : der= 5-(26,11,25536) and res= 5-(26,12,54720) - the given design is the derived.
- design 6-(27,12,25536) (# 13399) with respect to smaller t
- supplementary design of 6-(27,12,28728) (# 13401) with respect to smaller t
- residual design of 6-(28,12,35112) (# 13402)
- derived from 6-(28,13,80256) (# 13403)
- residual design of supplementary of 6-(28,12,39501) (# 13404)
- derived from supplementary of 6-(28,13,90288) (# 13405)

- clan: 15-(32,16,8), 6 times reduced t, 4 times derived
- Tran van Trung construction (right) for 5-(27,11,35112) (# 6840) : der= 5-(27,11,35112) and res= 5-(27,12,80256) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,12,80256) (# 6841) : der= 5-(27,11,35112) and res= 5-(27,12,80256) - the given design is the residual.
- design 6-(28,12,35112) (# 13402) with respect to smaller t
- supplementary design of 6-(28,12,39501) (# 13404) with respect to smaller t
- derived from 6-(29,13,115368) (# 13406)
- derived from supplementary of 6-(29,13,129789) (# 13408)

- clan: 15-(32,16,8), 6 times reduced t, 3 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(27,12,80256) (# 6841) : der= 5-(27,12,80256) and res= 5-(27,13,150480) - the given design is the derived.
- design 6-(28,13,80256) (# 13403) with respect to smaller t
- supplementary design of 6-(28,13,90288) (# 13405) with respect to smaller t
- residual design of 6-(29,13,115368) (# 13406)
- derived from 6-(29,14,230736) (# 13407)
- residual design of supplementary of 6-(29,13,129789) (# 13408)
- derived from supplementary of 6-(29,14,259578) (# 13409)

- clan: 15-(32,16,8), 7 times reduced t, 3 times derived
- Tran van Trung construction (right) for 5-(28,12,115368) (# 6842) : der= 5-(28,12,115368) and res= 5-(28,13,230736) - the given design is the derived.
- Tran van Trung construction (left) for 5-(28,13,230736) (# 6843) : der= 5-(28,12,115368) and res= 5-(28,13,230736) - the given design is the residual.
- design 6-(29,13,115368) (# 13406) with respect to smaller t
- supplementary design of 6-(29,13,129789) (# 13408) with respect to smaller t
- derived from 6-(30,14,346104) (# 13410)
- derived from supplementary of 6-(30,14,389367) (# 13413)

- clan: 15-(32,16,8), 7 times reduced t, 2 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(28,13,230736) (# 6843) : der= 5-(28,13,230736) and res= 5-(28,14,384560) - the given design is the derived.
- design 6-(29,14,230736) (# 13407) with respect to smaller t
- supplementary design of 6-(29,14,259578) (# 13409) with respect to smaller t
- residual design of 6-(30,14,346104) (# 13410)
- derived from 6-(30,15,615296) (# 13411)
- residual design of supplementary of 6-(30,14,389367) (# 13413)
- derived from supplementary of 6-(30,15,692208) (# 13414)

- clan: 15-(32,16,8), 8 times reduced t, 2 times derived
- Tran van Trung construction (right) for 5-(29,13,346104) (# 6844) : der= 5-(29,13,346104) and res= 5-(29,14,615296) - the given design is the derived.
- Tran van Trung construction (left) for 5-(29,14,615296) (# 6845) : der= 5-(29,13,346104) and res= 5-(29,14,615296) - the given design is the residual.
- design 6-(30,14,346104) (# 13410) with respect to smaller t
- supplementary design of 6-(30,14,389367) (# 13413) with respect to smaller t
- derived from 6-(31,15,961400) (# 13416)
- derived from supplementary of 6-(31,15,1081575) (# 13421)

- clan: 15-(32,16,8), 8 times reduced t, 1 times derived, 1 times residual
- Tran van Trung construction with complementary design for 5-(29,14,615296) (# 6845)
- design 6-(30,15,615296) (# 13411) with respect to smaller t
- supplementary design of 6-(30,15,692208) (# 13414) with respect to smaller t
- residual design of 6-(31,15,961400) (# 13416)
- Tran van Trung construction (left) for 5-(29,15,922944) (# 13417) : der= 5-(29,14,615296) and res= 5-(29,15,922944) - the given design is the residual.
- residual design of supplementary of 6-(31,15,1081575) (# 13421)
- derived from 6-(31,16,1538240) (# 13430)
- derived from supplementary of 6-(31,16,1730520) (# 13431)

- clan: 15-(32,16,8), 9 times reduced t, 1 times derived
- Tran van Trung construction (right) for 5-(30,14,961400) (# 6846) : der= 5-(30,14,961400) and res= 5-(30,15,1538240) - the given design is the derived.
- Tran van Trung construction (left) for 5-(30,15,1538240) (# 6847) : der= 5-(30,14,961400) and res= 5-(30,15,1538240) - the given design is the residual.
- design 6-(31,15,961400) (# 13416) with respect to smaller t
- supplementary design of 6-(31,15,1081575) (# 13421) with respect to smaller t
- derived from 6-(32,16,2499640) (# 13422)
- derived from supplementary of 6-(32,16,2812095) (# 13426)

- clan: 15-(32,16,8), 10 times reduced t
- Tran van Trung construction with complementary design for 5-(31,15,2499640) (# 6848)
- design 6-(32,16,2499640) (# 13422) with respect to smaller t
- supplementary design of 6-(32,16,2812095) (# 13426) with respect to smaller t
- Tran van Trung construction (left) for 5-(31,16,3635840) (# 13428) : der= 5-(31,15,2499640) and res= 5-(31,16,3635840) - the given design is the residual.

- clan: 11-(30,15,1830), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,1830), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1830) (# 6850) : der= 5-(24,9,1830) and res= 5-(24,10,5490) - the given design is the derived.

- clan: 17-(36,18,9), 9 times derived, 3 times residual
- $PGL(2,23)$ (>1 isomorphism types)
- residual design of 6-(25,9,459) (# 13782)
- residual design of supplementary of 6-(25,9,510) (# 13784)

- clan: 17-(36,18,9), 1 times reduced t, 9 times derived, 2 times residual
- Tran van Trung construction (left) for 5-(24,9,1836) (# 6852) : der= 5-(24,8,459) and res= 5-(24,9,1836) - the given design is the residual.
- derived from 6-(26,10,2295) (# 10524)
- residual design of 6-(26,9,540) (# 10588)
- residual design of supplementary of 6-(26,9,600) (# 10594)
- design 6-(25,9,459) (# 13782) with respect to smaller t
- supplementary design of 6-(25,9,510) (# 13784) with respect to smaller t
- derived from supplementary of 6-(26,10,2550) (# 13795)

- clan: 17-(36,18,9), 1 times reduced t, 8 times derived, 3 times residual
- Tran van Trung construction (right) for 5-(24,9,1836) (# 6852) : der= 5-(24,9,1836) and res= 5-(24,10,5508) - the given design is the derived.
- residual design of 6-(26,10,2295) (# 10524)
- residual design of supplementary of 6-(26,10,2550) (# 13795)
- derived from 6-(26,11,7344) (# 14309)
- derived from supplementary of 6-(26,11,8160) (# 14311)

- clan: 17-(36,18,9), 2 times reduced t, 9 times derived, 1 times residual
- Tran van Trung construction (left) for 5-(25,9,2295) (# 6853) : der= 5-(25,8,540) and res= 5-(25,9,2295) - the given design is the residual.
- $PGL(2,25)$
- design 6-(26,9,540) (# 10588) with respect to smaller t
- derived from 6-(27,10,2835) (# 10589)
- supplementary design of 6-(26,9,600) (# 10594) with respect to smaller t
- derived from supplementary of 6-(27,10,3150) (# 10600)
- residual design of 6-(27,9,630) (# 15114)
- residual design of supplementary of 6-(27,9,700) (# 15116)

- clan: 17-(36,18,9), 2 times reduced t, 8 times derived, 2 times residual
- Tran van Trung construction (right) for 5-(25,9,2295) (# 6853) : der= 5-(25,9,2295) and res= 5-(25,10,7344) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7344) (# 6854) : der= 5-(25,9,2295) and res= 5-(25,10,7344) - the given design is the residual.
- design 6-(26,10,2295) (# 10524) with respect to smaller t
- residual design of 6-(27,10,2835) (# 10589)
- residual design of supplementary of 6-(27,10,3150) (# 10600)
- derived from 6-(27,11,9639) (# 10759)
- supplementary design of 6-(26,10,2550) (# 13795) with respect to smaller t
- derived from supplementary of 6-(27,11,10710) (# 14310)

- clan: 17-(36,18,9), 3 times reduced t, 9 times derived
- Tran van Trung construction (left) for 5-(26,9,2835) (# 6855) : der= 5-(26,8,630) and res= 5-(26,9,2835) - the given design is the residual.
- $PGL(2,25)+$
- derived from 6-(28,10,3465) (# 15113)
- design 6-(27,9,630) (# 15114) with respect to smaller t
- derived from supplementary of 6-(28,10,3850) (# 15115)
- supplementary design of 6-(27,9,700) (# 15116) with respect to smaller t

- clan: 17-(36,18,9), 3 times reduced t, 8 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(26,9,2835) (# 6855) : der= 5-(26,9,2835) and res= 5-(26,10,9639) - the given design is the derived.
- Tran van Trung construction (left) for 5-(26,10,9639) (# 6856) : der= 5-(26,9,2835) and res= 5-(26,10,9639) - the given design is the residual.
- design 6-(27,10,2835) (# 10589) with respect to smaller t
- supplementary design of 6-(27,10,3150) (# 10600) with respect to smaller t
- derived from 6-(28,11,12474) (# 10764)
- derived from supplementary of 6-(28,11,13860) (# 14315)
- residual design of 6-(28,10,3465) (# 15113)
- residual design of supplementary of 6-(28,10,3850) (# 15115)

- clan: 17-(36,18,9), 4 times reduced t, 8 times derived
- Tran van Trung construction (right) for 5-(27,9,3465) (# 6857) : der= 5-(27,9,3465) and res= 5-(27,10,12474) - the given design is the derived.
- Tran van Trung construction (left) for 5-(27,10,12474) (# 6858) : der= 5-(27,9,3465) and res= 5-(27,10,12474) - the given design is the residual.
- design 6-(28,10,3465) (# 15113) with respect to smaller t
- supplementary design of 6-(28,10,3850) (# 15115) with respect to smaller t
- derived from 6-(29,11,15939) (# 15120)
- derived from supplementary of 6-(29,11,17710) (# 15122)

- clan: 11-(30,15,1842), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,1842), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1842) (# 6860) : der= 5-(24,9,1842) and res= 5-(24,10,5526) - the given design is the derived.

- clan: 13-(32,16,462), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,462), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1848) (# 6862) : der= 5-(24,8,462) and res= 5-(24,9,1848) - the given design is the residual.

- clan: 13-(32,16,462), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1848) (# 6862) : der= 5-(24,9,1848) and res= 5-(24,10,5544) - the given design is the derived.

- clan: 13-(32,16,462), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2310) (# 6863) : der= 5-(25,9,2310) and res= 5-(25,10,7392) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7392) (# 6864) : der= 5-(25,9,2310) and res= 5-(25,10,7392) - the given design is the residual.

- clan: 11-(30,15,1854), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1854), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1854) (# 6866) : der= 5-(24,9,1854) and res= 5-(24,10,5562) - the given design is the derived.

- clan: 11-(30,15,186), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,186), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,186) (# 6868) : der= 5-(24,9,186) and res= 5-(24,10,558) - the given design is the derived.

- clan: 13-(32,16,465), 7 times derived, 1 times residual
- $M_{11,12}\times id_2$
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
- residual design of 6-(25,9,465) (# 10464)

- clan: 13-(32,16,465), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1860) (# 6870) : der= 5-(24,8,465) and res= 5-(24,9,1860) - the given design is the residual.
- design 6-(25,9,465) (# 10464) with respect to smaller t
- derived from 6-(26,10,2325) (# 10530)
- derived from supplementary of 6-(26,10,2520) (# 14319)

- clan: 13-(32,16,465), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1860) (# 6870) : der= 5-(24,9,1860) and res= 5-(24,10,5580) - the given design is the derived.
- residual design of 6-(26,10,2325) (# 10530)
- derived from 6-(26,11,7440) (# 14317)
- residual design of supplementary of 6-(26,10,2520) (# 14319)
- derived from supplementary of 6-(26,11,8064) (# 14320)

- clan: 13-(32,16,465), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2325) (# 6871) : der= 5-(25,9,2325) and res= 5-(25,10,7440) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7440) (# 6872) : der= 5-(25,9,2325) and res= 5-(25,10,7440) - the given design is the residual.
- design 6-(26,10,2325) (# 10530) with respect to smaller t
- derived from 6-(27,11,9765) (# 10768)
- derived from supplementary of 6-(27,11,10584) (# 14318)
- supplementary design of 6-(26,10,2520) (# 14319) with respect to smaller t

- clan: 11-(30,15,1866), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1866), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1866) (# 6874) : der= 5-(24,9,1866) and res= 5-(24,10,5598) - the given design is the derived.

- clan: 13-(32,16,468), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,468), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1872) (# 6876) : der= 5-(24,8,468) and res= 5-(24,9,1872) - the given design is the residual.

- clan: 13-(32,16,468), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1872) (# 6876) : der= 5-(24,9,1872) and res= 5-(24,10,5616) - the given design is the derived.

- clan: 13-(32,16,468), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2340) (# 6877) : der= 5-(25,9,2340) and res= 5-(25,10,7488) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7488) (# 6878) : der= 5-(25,9,2340) and res= 5-(25,10,7488) - the given design is the residual.

- clan: 11-(30,15,1878), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,1878), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1878) (# 6880) : der= 5-(24,9,1878) and res= 5-(24,10,5634) - the given design is the derived.

- clan: 13-(32,16,471), 7 times derived, 1 times residual
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 13-(32,16,471), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1884) (# 6882) : der= 5-(24,8,471) and res= 5-(24,9,1884) - the given design is the residual.

- clan: 13-(32,16,471), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1884) (# 6882) : der= 5-(24,9,1884) and res= 5-(24,10,5652) - the given design is the derived.

- clan: 13-(32,16,471), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2355) (# 6883) : der= 5-(25,9,2355) and res= 5-(25,10,7536) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7536) (# 6884) : der= 5-(25,9,2355) and res= 5-(25,10,7536) - the given design is the residual.

- clan: 11-(30,15,1890), 6 times derived
- $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

- clan: 11-(30,15,1890), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1890) (# 6886) : der= 5-(24,9,1890) and res= 5-(24,10,5670) - the given design is the derived.

- clan: 13-(32,16,474), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)
- derived from 6-(25,10,1896) (# 13664)
- derived from supplementary of 6-(25,10,1980) (# 13667)

- clan: 13-(32,16,474), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1896) (# 6888) : der= 5-(24,8,474) and res= 5-(24,9,1896) - the given design is the residual.

- clan: 13-(32,16,474), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1896) (# 6888) : der= 5-(24,9,1896) and res= 5-(24,10,5688) - the given design is the derived.
- derived from 6-(26,11,7584) (# 13663)
- design 6-(25,10,1896) (# 13664) with respect to smaller t
- derived from supplementary of 6-(26,11,7920) (# 13666)
- supplementary design of 6-(25,10,1980) (# 13667) with respect to smaller t

- clan: 13-(32,16,474), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2370) (# 6889) : der= 5-(25,9,2370) and res= 5-(25,10,7584) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7584) (# 6890) : der= 5-(25,9,2370) and res= 5-(25,10,7584) - the given design is the residual.

- clan: 11-(30,15,1902), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,1902), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1902) (# 6892) : der= 5-(24,9,1902) and res= 5-(24,10,5706) - the given design is the derived.

- clan: 13-(32,16,477), 7 times derived, 1 times residual
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 13-(32,16,477), 1 times reduced t, 7 times derived
- Tran van Trung construction (left) for 5-(24,9,1908) (# 6894) : der= 5-(24,8,477) and res= 5-(24,9,1908) - the given design is the residual.
- derived from 6-(26,10,2385) (# 14324)
- derived from supplementary of 6-(26,10,2460) (# 14327)

- clan: 13-(32,16,477), 1 times reduced t, 6 times derived, 1 times residual
- Tran van Trung construction (right) for 5-(24,9,1908) (# 6894) : der= 5-(24,9,1908) and res= 5-(24,10,5724) - the given design is the derived.
- residual design of 6-(26,10,2385) (# 14324)
- derived from 6-(26,11,7632) (# 14325)
- residual design of supplementary of 6-(26,10,2460) (# 14327)
- derived from supplementary of 6-(26,11,7872) (# 14328)

- clan: 13-(32,16,477), 2 times reduced t, 6 times derived
- Tran van Trung construction (right) for 5-(25,9,2385) (# 6895) : der= 5-(25,9,2385) and res= 5-(25,10,7632) - the given design is the derived.
- Tran van Trung construction (left) for 5-(25,10,7632) (# 6896) : der= 5-(25,9,2385) and res= 5-(25,10,7632) - the given design is the residual.
- derived from 6-(27,11,10017) (# 10605)
- design 6-(26,10,2385) (# 14324) with respect to smaller t
- derived from supplementary of 6-(27,11,10332) (# 14326)
- supplementary design of 6-(26,10,2460) (# 14327) with respect to smaller t

- clan: 11-(30,15,1914), 6 times derived
- $PGL(2,23)$ (>1 isomorphism types)

- clan: 11-(30,15,1914), 1 times reduced t, 5 times derived
- Tran van Trung construction (right) for 5-(24,9,1914) (# 6898) : der= 5-(24,9,1914) and res= 5-(24,10,5742) - the given design is the derived.

created: Fri Oct 23 11:10:24 CEST 2009