t designs with small t, id ge 5700

clan: 6-(25,8,84), 1 times reduced t
Tran van Trung construction (left) for 5-(24,8,476) (# 5718) : der= 5-(24,7,84) and res= 5-(24,8,476) - the given design is the residual.

# 5720: 5-(24,8,477)

clan: 13-(32,16,477), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5721: 5-(24,8,478)

clan: 5-(24,8,478)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5722: 5-(24,8,479)

clan: 5-(24,8,479)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5723: 5-(24,8,48)

clan: 13-(32,16,48), 8 times derived
$PGL(2,23)$ 217 isomorphism types

# 5724: 5-(24,8,480)

clan: 13-(32,16,480), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5725: 5-(24,8,481)

clan: 5-(24,8,481)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5726: 5-(24,8,482)

clan: 5-(24,8,482)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5727: 5-(24,8,483)

clan: 13-(32,16,483), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5728: 5-(24,8,484)

clan: 5-(24,8,484)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5729: 5-(24,8,485)

clan: 5-(24,8,485)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5730: 5-(24,8,486)

clan: 13-(32,16,486), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5731: 5-(24,8,487)

clan: 5-(24,8,487)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5732: 5-(24,8,488)

clan: 5-(24,8,488)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5733: 5-(24,8,489)

clan: 13-(32,16,489), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5734: 5-(24,8,49)

clan: 5-(24,8,49)
$PGL(2,23)$ 21 isomorphism types

# 5735: 5-(24,8,490)

clan: 5-(24,8,490)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5736: 5-(24,8,491)

clan: 5-(24,8,491)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5737: 5-(24,8,492)

clan: 13-(32,16,492), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5738: 5-(24,8,493)

clan: 6-(25,8,87), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5739: 5-(24,8,494)

clan: 6-(24,8,78), 1 times reduced t
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5740: 5-(24,8,495)

clan: 13-(32,16,495), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5741: 5-(24,8,496)

clan: 5-(24,8,496)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5742: 5-(24,8,497)

clan: 5-(24,8,497)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5743: 5-(24,8,498)

clan: 13-(32,16,498), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5744: 5-(24,8,499)

clan: 5-(24,8,499)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5745: 5-(24,8,5)

clan: 5-(24,8,5)
\cite{KramerMagliveras74}

# 5746: 5-(24,8,50)

clan: 5-(24,8,50)
$PGL(2,23)$ 231 isomorphism types

# 5747: 5-(24,8,500)

clan: 5-(24,8,500)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5748: 5-(24,8,501)

clan: 13-(32,16,501), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5749: 5-(24,8,502)

clan: 5-(24,8,502)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5750: 5-(24,8,503)

clan: 5-(24,8,503)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5751: 5-(24,8,504)

clan: 13-(32,16,504), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from supplementary of 6-(25,9,465) (# 10464)

# 5752: 5-(24,8,505)

clan: 5-(24,8,505)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5753: 5-(24,8,506)

clan: 5-(24,8,506)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5754: 5-(24,8,507)

clan: 13-(32,16,507), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5755: 5-(24,8,508)

clan: 5-(24,8,508)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5756: 5-(24,8,509)

clan: 5-(24,8,509)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5757: 5-(24,8,51)

clan: 17-(36,18,1), 10 times derived, 2 times residual
$PGL(2,23)$ 27 isomorphism types

# 5758: 5-(25,8,60)

clan: 17-(36,18,1), 1 times reduced t, 10 times derived, 1 times residual
Tran van Trung construction (left) for 5-(24,8,51) (# 5757) : der= 5-(24,7,9) and res= 5-(24,8,51) - the given design is the residual.
derived from 6-(26,9,60) (# 10590)

# 5759: 5-(26,8,70)

clan: 17-(36,18,1), 2 times reduced t, 10 times derived
Tran van Trung construction (left) for 5-(25,8,60) (# 5758) : der= 5-(25,7,10) and res= 5-(25,8,60) - the given design is the residual.
$PSL(2,25)$

# 5760: 5-(24,8,510)

clan: 17-(36,18,10), 10 times derived, 2 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
residual design of supplementary of 6-(25,8,81) (# 10411)
derived from supplementary of 6-(25,9,459) (# 13782)
residual design of 6-(25,8,90) (# 13783)
derived from 6-(25,9,510) (# 13784)

# 5761: 5-(24,8,511)

clan: 5-(24,8,511)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5762: 5-(24,8,512)

clan: 5-(24,8,512)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5763: 5-(24,8,513)

clan: 15-(32,16,9), 2 times reduced t, 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
supplementary design of 6-(24,8,72) (# 9851) with respect to smaller t
Tran van Trung construction (right) for 5-(23,7,81) (# 9854) : der= 5-(23,7,81) and res= 5-(23,8,432) - the given design is the derived.
Tran van Trung construction (left) for 5-(23,8,432) (# 9855) : der= 5-(23,7,81) and res= 5-(23,8,432) - the given design is the residual.
design 6-(24,8,81) (# 13382) with respect to smaller t
derived from supplementary of 6-(25,9,456) (# 13391)
derived from 6-(25,9,513) (# 13393)