t designs with small t, id ge 5500

---

# 5500: 5-(24,8,293)

• clan: 5-(24,8,293)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5501: 5-(24,8,294)

• clan: 13-(32,16,294), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5502: 5-(24,8,295)

• clan: 5-(24,8,295)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5503: 5-(24,8,296)

• clan: 5-(24,8,296)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5504: 5-(24,8,297)

• clan: 13-(32,16,297), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5505: 5-(24,8,298)

• clan: 5-(24,8,298)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5506: 5-(24,8,299)

• clan: 5-(24,8,299)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5507: 5-(24,8,3)

• clan: 13-(32,16,3), 8 times derived
• \cite{KramerMagliveras74}

---

# 5508: 5-(24,8,30)

• clan: 13-(32,16,30), 8 times derived
• $PGL(2,23)$ 4 isomorphism types

---

# 5509: 5-(24,8,300)

• clan: 13-(32,16,300), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5510: 5-(24,8,301)

• clan: 5-(24,8,301)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5511: 5-(24,8,302)

• clan: 5-(24,8,302)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5512: 5-(24,8,303)

• clan: 13-(32,16,303), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5513: 5-(24,8,304)

• clan: 6-(24,8,48), 1 times reduced t
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5514: 5-(24,8,305)

• clan: 5-(24,8,305)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5515: 5-(24,8,306)

• clan: 17-(36,18,6), 10 times derived, 2 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• residual design of 6-(25,8,54) (# 10402)
• residual design of supplementary of 6-(25,8,117) (# 13766)
• derived from 6-(25,9,306) (# 13769)
• derived from supplementary of 6-(25,9,663) (# 13771)

---

# 5516: 5-(25,8,360)

• clan: 17-(36,18,6), 1 times reduced t, 10 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(24,8,306) (# 5515) : der= 5-(24,7,54) and res= 5-(24,8,306) - the given design is the residual.
• design 6-(25,8,54) (# 10402) with respect to smaller t
• residual design of 6-(26,8,60) (# 10562)
• derived from 6-(26,9,360) (# 10575)
• residual design of supplementary of 6-(26,8,130) (# 13764)
• supplementary design of 6-(25,8,117) (# 13766) with respect to smaller t
• derived from supplementary of 6-(26,9,780) (# 13770)

---

# 5517: 5-(26,8,420)

• 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

---

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