t designs with small t, id ge 5600

---

# 5600: 5-(24,8,376)

• clan: 5-(24,8,376)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5601: 5-(24,8,377)

• clan: 5-(24,8,377)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5602: 5-(24,8,378)

• clan: 13-(32,16,378), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5603: 5-(24,8,379)

• clan: 5-(24,8,379)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5604: 5-(24,8,38)

• clan: 6-(24,8,6), 1 times reduced t
• $PGL(2,23)$ 24 isomorphism types

---

# 5605: 5-(24,8,380)

• clan: 6-(24,8,60), 1 times reduced t
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5606: 5-(24,8,381)

• clan: 13-(32,16,381), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5607: 5-(24,8,382)

• clan: 5-(24,8,382)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5608: 5-(24,8,383)

• clan: 5-(24,8,383)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5609: 5-(24,8,384)

• clan: 13-(32,16,384), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• derived from 6-(25,9,384) (# 10452)

---

# 5610: 5-(24,8,385)

• clan: 5-(24,8,385)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5611: 5-(24,8,386)

• clan: 5-(24,8,386)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5612: 5-(24,8,387)

• clan: 13-(32,16,387), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5613: 5-(24,8,388)

• clan: 5-(24,8,388)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5614: 5-(24,8,389)

• clan: 5-(24,8,389)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5615: 5-(24,8,39)

• clan: 13-(32,16,39), 8 times derived
• $PGL(2,23)$ 4 isomorphism types

---

# 5616: 5-(24,8,390)

• clan: 13-(32,16,390), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5617: 5-(24,8,391)

• clan: 6-(25,8,69), 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5618: 5-(25,8,460)

• clan: 6-(25,8,69), 1 times reduced t
• Tran van Trung construction (left) for 5-(24,8,391) (# 5617) : der= 5-(24,7,69) and res= 5-(24,8,391) - the given design is the residual.

---

# 5619: 5-(24,8,392)

• clan: 5-(24,8,392)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5620: 5-(24,8,393)

• clan: 13-(32,16,393), 8 times derived
• $M_{11,12}\times id_2$
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5621: 5-(24,8,394)

• clan: 5-(24,8,394)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5622: 5-(24,8,395)

• clan: 5-(24,8,395)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5623: 5-(24,8,396)

• clan: 13-(32,16,396), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5624: 5-(24,8,397)

• clan: 5-(24,8,397)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5625: 5-(24,8,398)

• clan: 5-(24,8,398)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5626: 5-(24,8,399)

• clan: 15-(32,16,7), 2 times reduced t, 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• design 6-(24,8,63) (# 9846) with respect to smaller t
• Tran van Trung construction (right) for 5-(23,7,63) (# 9847) : der= 5-(23,7,63) and res= 5-(23,8,336) - the given design is the derived.
• Tran van Trung construction (left) for 5-(23,8,336) (# 9848) : der= 5-(23,7,63) and res= 5-(23,8,336) - the given design is the residual.
• supplementary design of 6-(24,8,90) (# 13371) with respect to smaller t

---

# 5627: 5-(24,8,4)

• clan: 5-(24,8,4)
• \cite{KramerMagliveras74}

---

# 5628: 5-(24,8,40)

• clan: 5-(24,8,40)
• $PGL(2,23)$ 58 isomorphism types

---

# 5629: 5-(24,8,400)

• clan: 5-(24,8,400)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5630: 5-(24,8,401)

• clan: 5-(24,8,401)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5631: 5-(24,8,402)

• clan: 13-(32,16,402), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5632: 5-(24,8,403)

• clan: 5-(24,8,403)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5633: 5-(24,8,404)

• clan: 5-(24,8,404)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5634: 5-(24,8,405)

• clan: 13-(32,16,405), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• derived from 6-(25,9,405) (# 10455)

---

# 5635: 5-(24,8,406)

• clan: 5-(24,8,406)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5636: 5-(24,8,407)

• clan: 5-(24,8,407)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5637: 5-(24,8,408)

• clan: 17-(36,18,8), 10 times derived, 2 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• residual design of 6-(25,8,72) (# 10408)

---

# 5638: 5-(25,8,480)

• clan: 17-(36,18,8), 1 times reduced t, 10 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(24,8,408) (# 5637) : der= 5-(24,7,72) and res= 5-(24,8,408) - the given design is the residual.
• design 6-(25,8,72) (# 10408) with respect to smaller t
• derived from 6-(26,9,480) (# 10585)

---

# 5639: 5-(26,8,560)

• clan: 17-(36,18,8), 2 times reduced t, 10 times derived
• Tran van Trung construction (left) for 5-(25,8,480) (# 5638) : der= 5-(25,7,80) and res= 5-(25,8,480) - the given design is the residual.
• $PSL(2,25)$

---

# 5640: 5-(24,8,409)

• clan: 5-(24,8,409)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5641: 5-(24,8,41)

• clan: 5-(24,8,41)
• $PGL(2,23)$ 7 isomorphism types

---

# 5642: 5-(24,8,410)

• clan: 5-(24,8,410)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5643: 5-(24,8,411)

• clan: 13-(32,16,411), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5644: 5-(24,8,412)

• clan: 5-(24,8,412)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5645: 5-(24,8,413)

• clan: 5-(24,8,413)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5646: 5-(24,8,414)

• clan: 13-(32,16,414), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5647: 5-(24,8,415)

• clan: 5-(24,8,415)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5648: 5-(24,8,416)

• clan: 5-(24,8,416)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5649: 5-(24,8,417)

• clan: 13-(32,16,417), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5650: 5-(24,8,418)

• clan: 6-(24,8,66), 1 times reduced t
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5651: 5-(24,8,419)

• clan: 5-(24,8,419)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5652: 5-(24,8,42)

• clan: 13-(32,16,42), 8 times derived
• $PGL(2,23)$ 55 isomorphism types

---

# 5653: 5-(24,8,420)

• clan: 13-(32,16,420), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• derived from 6-(25,9,420) (# 10458)

---

# 5654: 5-(24,8,421)

• clan: 5-(24,8,421)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5655: 5-(24,8,422)

• clan: 5-(24,8,422)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5656: 5-(24,8,423)

• clan: 13-(32,16,423), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5657: 5-(24,8,424)

• clan: 5-(24,8,424)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5658: 5-(24,8,425)

• clan: 6-(25,8,75), 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5659: 5-(25,8,500)

• clan: 6-(25,8,75), 1 times reduced t
• Tran van Trung construction (left) for 5-(24,8,425) (# 5658) : der= 5-(24,7,75) and res= 5-(24,8,425) - the given design is the residual.

---

# 5660: 5-(24,8,426)

• clan: 13-(32,16,426), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5661: 5-(24,8,427)

• clan: 5-(24,8,427)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5662: 5-(24,8,428)

• clan: 5-(24,8,428)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5663: 5-(24,8,429)

• clan: 13-(32,16,429), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• derived from 6-(25,9,429) (# 10461)

---

# 5664: 5-(24,8,43)

• clan: 5-(24,8,43)
• $PGL(2,23)$ 6 isomorphism types

---

# 5665: 5-(24,8,430)

• clan: 5-(24,8,430)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5666: 5-(24,8,431)

• clan: 5-(24,8,431)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5667: 5-(24,8,432)

• clan: 13-(32,16,432), 8 times derived
• $M_{11,12}\times id_2$
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• derived from 6-(25,9,432) (# 17530)
• derived from supplementary of 6-(25,9,537) (# 17532)

---

# 5668: 5-(24,8,433)

• clan: 5-(24,8,433)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5669: 5-(24,8,434)

• clan: 5-(24,8,434)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5670: 5-(24,8,435)

• clan: 13-(32,16,435), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5671: 5-(24,8,436)

• clan: 5-(24,8,436)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5672: 5-(24,8,437)

• clan: 6-(24,8,69), 1 times reduced t
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5673: 5-(24,8,438)

• clan: 13-(32,16,438), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5674: 5-(24,8,439)

• clan: 5-(24,8,439)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5675: 5-(24,8,44)

• clan: 5-(24,8,44)
• $PGL(2,23)$ 48 isomorphism types

---

# 5676: 5-(24,8,440)

• clan: 5-(24,8,440)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5677: 5-(24,8,441)

• clan: 13-(32,16,441), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5678: 5-(24,8,442)

• clan: 6-(25,8,78), 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5679: 5-(25,8,520)

• clan: 6-(25,8,78), 1 times reduced t
• Tran van Trung construction (left) for 5-(24,8,442) (# 5678) : der= 5-(24,7,78) and res= 5-(24,8,442) - the given design is the residual.

---

# 5680: 5-(24,8,443)

• clan: 5-(24,8,443)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5681: 5-(24,8,444)

• clan: 13-(32,16,444), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5682: 5-(24,8,445)

• clan: 5-(24,8,445)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5683: 5-(24,8,446)

• clan: 5-(24,8,446)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5684: 5-(24,8,447)

• clan: 13-(32,16,447), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5685: 5-(24,8,448)

• clan: 5-(24,8,448)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5686: 5-(24,8,449)

• clan: 5-(24,8,449)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5687: 5-(24,8,45)

• clan: 13-(32,16,45), 8 times derived
• $PGL(2,23)$ 4 isomorphism types

---

# 5688: 5-(24,8,450)

• clan: 13-(32,16,450), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5689: 5-(24,8,451)

• clan: 5-(24,8,451)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5690: 5-(24,8,452)

• clan: 5-(24,8,452)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5691: 5-(24,8,453)

• clan: 13-(32,16,453), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5692: 5-(24,8,454)

• clan: 5-(24,8,454)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5693: 5-(24,8,455)

• clan: 5-(24,8,455)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5694: 5-(24,8,456)

• clan: 15-(32,16,8), 2 times reduced t, 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• design 6-(24,8,72) (# 9851) with respect to smaller t
• Tran van Trung construction (right) for 5-(23,7,72) (# 9852) : der= 5-(23,7,72) and res= 5-(23,8,384) - the given design is the derived.
• Tran van Trung construction (left) for 5-(23,8,384) (# 9853) : der= 5-(23,7,72) and res= 5-(23,8,384) - the given design is the residual.
• supplementary design of 6-(24,8,81) (# 13382) with respect to smaller t
• derived from 6-(25,9,456) (# 13391)
• derived from supplementary of 6-(25,9,513) (# 13393)

---

# 5695: 5-(24,8,457)

• clan: 5-(24,8,457)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5696: 5-(24,8,458)

• clan: 5-(24,8,458)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5697: 5-(24,8,459)

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

---

# 5698: 5-(25,8,540)

• clan: 17-(36,18,9), 1 times reduced t, 10 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(24,8,459) (# 5697) : der= 5-(24,7,81) and res= 5-(24,8,459) - the given design is the residual.
• design 6-(25,8,81) (# 10411) with respect to smaller t
• derived from 6-(26,9,540) (# 10588)
• derived from supplementary of 6-(26,9,600) (# 10594)
• supplementary design of 6-(25,8,90) (# 13783) with respect to smaller t

---

# 5699: 5-(26,8,630)

• clan: 17-(36,18,9), 2 times reduced t, 10 times derived
• Tran van Trung construction (left) for 5-(25,8,540) (# 5698) : der= 5-(25,7,90) and res= 5-(25,8,540) - the given design is the residual.
• $PSL(2,25)$
• derived from 6-(27,9,630) (# 15114)
• derived from supplementary of 6-(27,9,700) (# 15116)

---

---

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