clan: 17-(36,18,6), 2 times reduced t, 10 times derived
Tran van Trung construction (left) for 5-(25,8,360) (# 5516) : der= 5-(25,7,60) and res= 5-(25,8,360) - the given design is the residual.
$PSL(2,25)$
design 6-(26,8,60) (# 10562) with respect to smaller t
derived from 6-(27,9,420) (# 10578)
supplementary design of 6-(26,8,130) (# 13764) with respect to smaller t
derived from supplementary of 6-(27,9,910) (# 13774)

# 5518: 5-(24,8,307)

clan: 5-(24,8,307)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5519: 5-(24,8,308)

clan: 5-(24,8,308)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5520: 5-(24,8,309)

clan: 13-(32,16,309), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5521: 5-(24,8,31)

clan: 5-(24,8,31)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5522: 5-(24,8,310)

clan: 5-(24,8,310)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5523: 5-(24,8,311)

clan: 5-(24,8,311)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5524: 5-(24,8,312)

clan: 13-(32,16,312), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5525: 5-(24,8,313)

clan: 5-(24,8,313)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5526: 5-(24,8,314)

clan: 5-(24,8,314)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5527: 5-(24,8,315)

clan: 13-(32,16,315), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5528: 5-(24,8,316)

clan: 5-(24,8,316)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5529: 5-(24,8,317)

clan: 5-(24,8,317)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5530: 5-(24,8,318)

clan: 13-(32,16,318), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5531: 5-(24,8,319)

clan: 5-(24,8,319)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5532: 5-(24,8,32)

clan: 5-(24,8,32)
$PGL(2,23)$ 8 isomorphism types

# 5533: 5-(24,8,320)

clan: 5-(24,8,320)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5534: 5-(24,8,321)

clan: 13-(32,16,321), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5535: 5-(24,8,322)

clan: 5-(24,8,322)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5536: 5-(24,8,323)

clan: 7-(25,8,6), 1 times reduced t, 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5537: 5-(25,8,380)

clan: 7-(25,8,6), 2 times reduced t
Tran van Trung construction (left) for 5-(24,8,323) (# 5536) : der= 5-(24,7,57) and res= 5-(24,8,323) - the given design is the residual.

# 5538: 5-(24,8,324)

clan: 13-(32,16,324), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from 6-(25,9,324) (# 10443)

# 5539: 5-(24,8,325)

clan: 5-(24,8,325)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5540: 5-(24,8,326)

clan: 5-(24,8,326)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5541: 5-(24,8,327)

clan: 13-(32,16,327), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5542: 5-(24,8,328)

clan: 5-(24,8,328)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5543: 5-(24,8,329)

clan: 5-(24,8,329)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5544: 5-(24,8,33)

clan: 13-(32,16,33), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5545: 5-(24,8,330)

clan: 13-(32,16,330), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5546: 5-(24,8,331)

clan: 5-(24,8,331)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5547: 5-(24,8,332)

clan: 5-(24,8,332)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5548: 5-(24,8,333)

clan: 13-(32,16,333), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5549: 5-(24,8,334)

clan: 5-(24,8,334)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5550: 5-(24,8,335)

clan: 5-(24,8,335)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5551: 5-(24,8,336)

clan: 13-(32,16,336), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5552: 5-(24,8,337)

clan: 5-(24,8,337)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5553: 5-(24,8,338)

clan: 5-(24,8,338)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5554: 5-(24,8,339)

clan: 13-(32,16,339), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5555: 5-(24,8,34)

clan: 6-(25,8,6), 1 times residual
$PGL(2,23)$ 9 isomorphism types

# 5556: 5-(25,8,40)

clan: 6-(25,8,6), 1 times reduced t
Tran van Trung construction (left) for 5-(24,8,34) (# 5555) : der= 5-(24,7,6) and res= 5-(24,8,34) - the given design is the residual.

# 5557: 5-(24,8,340)

clan: 6-(25,8,60), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5558: 5-(25,8,400)

clan: 6-(25,8,60), 1 times reduced t
Tran van Trung construction (left) for 5-(24,8,340) (# 5557) : der= 5-(24,7,60) and res= 5-(24,8,340) - the given design is the residual.

# 5559: 5-(24,8,341)

clan: 5-(24,8,341)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5560: 5-(24,8,342)

clan: 15-(32,16,6), 2 times reduced t, 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
design 6-(24,8,54) (# 9841) with respect to smaller t
Tran van Trung construction (right) for 5-(23,7,54) (# 9842) : der= 5-(23,7,54) and res= 5-(23,8,288) - the given design is the derived.
Tran van Trung construction (left) for 5-(23,8,288) (# 9843) : der= 5-(23,7,54) and res= 5-(23,8,288) - the given design is the residual.
supplementary design of 6-(24,8,99) (# 13317) with respect to smaller t
derived from 6-(25,9,342) (# 13325)
derived from supplementary of 6-(25,9,627) (# 13327)

# 5561: 5-(24,8,343)

clan: 5-(24,8,343)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5562: 5-(24,8,344)

clan: 5-(24,8,344)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5563: 5-(24,8,345)

clan: 13-(32,16,345), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5564: 5-(24,8,346)

clan: 5-(24,8,346)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5565: 5-(24,8,347)

clan: 5-(24,8,347)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5566: 5-(24,8,348)

clan: 13-(32,16,348), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5567: 5-(24,8,349)

clan: 5-(24,8,349)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5568: 5-(24,8,35)

clan: 5-(24,8,35)
$PGL(2,23)$ 1 isomorphism type

# 5569: 5-(24,8,350)

clan: 5-(24,8,350)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5570: 5-(24,8,351)

clan: 13-(32,16,351), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5571: 5-(24,8,352)

clan: 5-(24,8,352)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5572: 5-(24,8,353)

clan: 5-(24,8,353)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5573: 5-(24,8,354)

clan: 13-(32,16,354), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5574: 5-(24,8,355)

clan: 5-(24,8,355)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5575: 5-(24,8,356)

clan: 5-(24,8,356)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5576: 5-(24,8,357)

clan: 17-(36,18,7), 10 times derived, 2 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
residual design of 6-(25,8,63) (# 10405)
derived from 6-(25,9,357) (# 13776)
residual design of supplementary of 6-(25,8,108) (# 13778)
derived from supplementary of 6-(25,9,612) (# 13779)

# 5577: 5-(25,8,420)

clan: 17-(36,18,7), 1 times reduced t, 10 times derived, 1 times residual
Tran van Trung construction (left) for 5-(24,8,357) (# 5576) : der= 5-(24,7,63) and res= 5-(24,8,357) - the given design is the residual.
design 6-(25,8,63) (# 10405) with respect to smaller t
residual design of 6-(26,8,70) (# 10565)
derived from 6-(26,9,420) (# 10580)
derived from supplementary of 6-(26,9,720) (# 13777)
supplementary design of 6-(25,8,108) (# 13778) with respect to smaller t

# 5578: 5-(26,8,490)

clan: 17-(36,18,7), 2 times reduced t, 10 times derived
Tran van Trung construction (left) for 5-(25,8,420) (# 5577) : der= 5-(25,7,70) and res= 5-(25,8,420) - the given design is the residual.
design 6-(26,8,70) (# 10565) with respect to smaller t
derived from 6-(27,9,490) (# 10583)

# 5579: 5-(24,8,358)

clan: 5-(24,8,358)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5580: 5-(24,8,359)

clan: 5-(24,8,359)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5581: 5-(24,8,36)

clan: 13-(32,16,36), 8 times derived
$PGL(2,23)$ 13 isomorphism types

# 5582: 5-(24,8,360)

clan: 13-(32,16,360), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from 6-(25,9,360) (# 10446)

# 5583: 5-(24,8,361)

clan: 6-(24,8,57), 1 times reduced t
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5584: 5-(24,8,362)

clan: 5-(24,8,362)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5585: 5-(24,8,363)

clan: 13-(32,16,363), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5586: 5-(24,8,364)

clan: 5-(24,8,364)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5587: 5-(24,8,365)

clan: 5-(24,8,365)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5588: 5-(24,8,366)

clan: 13-(32,16,366), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5589: 5-(24,8,367)

clan: 5-(24,8,367)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5590: 5-(24,8,368)

clan: 5-(24,8,368)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5591: 5-(24,8,369)

clan: 13-(32,16,369), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
derived from 6-(25,9,369) (# 10449)

# 5592: 5-(24,8,37)

clan: 5-(24,8,37)
$PGL(2,23)$ 1 isomorphism type

# 5593: 5-(24,8,370)

clan: 5-(24,8,370)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5594: 5-(24,8,371)

clan: 5-(24,8,371)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5595: 5-(24,8,372)

clan: 13-(32,16,372), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5596: 5-(24,8,373)

clan: 5-(24,8,373)
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5597: 5-(24,8,374)

clan: 6-(25,8,66), 1 times residual
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

# 5598: 5-(25,8,440)

clan: 6-(25,8,66), 1 times reduced t
Tran van Trung construction (left) for 5-(24,8,374) (# 5597) : der= 5-(24,7,66) and res= 5-(24,8,374) - the given design is the residual.

# 5599: 5-(24,8,375)

clan: 13-(32,16,375), 8 times derived
$ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

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