t designs with small t, id ge 5300

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# 5300: 5-(24,8,124)

• clan: 5-(24,8,124)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5301: 5-(24,8,125)

• clan: 5-(24,8,125)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5302: 5-(24,8,126)

• clan: 13-(32,16,126), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

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# 5303: 5-(24,8,127)

• clan: 5-(24,8,127)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5304: 5-(24,8,128)

• clan: 5-(24,8,128)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• \cite{Driessen78} $M_{24}$ 1 isomorphism type

---

# 5305: 5-(24,8,129)

• clan: 13-(32,16,129), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• \cite{Driessen78} $M_{24}$ 1 isomorphism type

---

# 5306: 5-(24,8,130)

• clan: 5-(24,8,130)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5307: 5-(24,8,131)

• clan: 5-(24,8,131)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5308: 5-(24,8,132)

• clan: 13-(32,16,132), 8 times derived
• $PGL(2,23)$

---

# 5309: 5-(24,8,133)

• clan: 6-(24,8,21), 1 times reduced t
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5310: 5-(24,8,134)

• clan: 5-(24,8,134)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5311: 5-(24,8,135)

• clan: 13-(32,16,135), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5312: 5-(24,8,136)

• clan: 6-(25,8,24), 1 times residual
• $PGL(2,23)$

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# 5313: 5-(25,8,160)

• clan: 6-(25,8,24), 1 times reduced t
• Tran van Trung construction (left) for 5-(24,8,136) (# 5312) : der= 5-(24,7,24) and res= 5-(24,8,136) - the given design is the residual.

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# 5314: 5-(24,8,137)

• clan: 5-(24,8,137)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5315: 5-(24,8,138)

• clan: 13-(32,16,138), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5316: 5-(24,8,139)

• clan: 5-(24,8,139)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5317: 5-(24,8,140)

• clan: 5-(24,8,140)
• $PGL(2,23)$

---

# 5318: 5-(24,8,141)

• clan: 13-(32,16,141), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5319: 5-(24,8,142)

• clan: 5-(24,8,142)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5320: 5-(24,8,143)

• clan: 5-(24,8,143)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5321: 5-(24,8,144)

• clan: 13-(32,16,144), 8 times derived
• $PGL(2,23)$
• derived from 6-(25,9,144) (# 10417)

---

# 5322: 5-(24,8,145)

• clan: 5-(24,8,145)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5323: 5-(24,8,146)

• clan: 5-(24,8,146)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5324: 5-(24,8,147)

• clan: 13-(32,16,147), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5325: 5-(24,8,148)

• clan: 5-(24,8,148)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5326: 5-(24,8,149)

• clan: 5-(24,8,149)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5327: 5-(24,8,150)

• clan: 13-(32,16,150), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5328: 5-(24,8,151)

• clan: 5-(24,8,151)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5329: 5-(24,8,152)

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

---

# 5330: 5-(24,8,153)

• clan: 17-(36,18,3), 10 times derived, 2 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5331: 5-(25,8,180)

• clan: 17-(36,18,3), 1 times reduced t, 10 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(24,8,153) (# 5330) : der= 5-(24,7,27) and res= 5-(24,8,153) - the given design is the residual.
• derived from 6-(26,9,180) (# 10568)

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# 5332: 5-(26,8,210)

• clan: 17-(36,18,3), 2 times reduced t, 10 times derived
• Tran van Trung construction (left) for 5-(25,8,180) (# 5331) : der= 5-(25,7,30) and res= 5-(25,8,180) - the given design is the residual.
• $PSL(2,25)$

---

# 5333: 5-(24,8,154)

• clan: 5-(24,8,154)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5334: 5-(24,8,155)

• clan: 5-(24,8,155)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5335: 5-(24,8,156)

• clan: 13-(32,16,156), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• $PGL(2,23)$

---

# 5336: 5-(24,8,157)

• clan: 5-(24,8,157)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5337: 5-(24,8,158)

• clan: 5-(24,8,158)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5338: 5-(24,8,159)

• clan: 13-(32,16,159), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5339: 5-(24,8,16)

• clan: 5-(24,8,16)
• $PSL(2,23)$ 2 isomorphism types

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# 5340: 5-(24,8,160)

• clan: 5-(24,8,160)
• $PGL(2,23)$

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# 5341: 5-(24,8,161)

• clan: 5-(24,8,161)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5342: 5-(24,8,162)

• clan: 13-(32,16,162), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5343: 5-(24,8,163)

• clan: 5-(24,8,163)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5344: 5-(24,8,164)

• clan: 5-(24,8,164)
• $PGL(2,23)$

---

# 5345: 5-(24,8,165)

• clan: 13-(32,16,165), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5346: 5-(24,8,166)

• clan: 5-(24,8,166)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5347: 5-(24,8,167)

• clan: 5-(24,8,167)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5348: 5-(24,8,168)

• clan: 13-(32,16,168), 8 times derived
• $PGL(2,23)$

---

# 5349: 5-(24,8,169)

• clan: 5-(24,8,169)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5350: 5-(24,8,17)

• clan: 6-(25,8,3), 1 times residual
• $PSL(2,23)$ 4 isomorphism types

---

# 5351: 5-(25,8,20)

• clan: 6-(25,8,3), 1 times reduced t
• Tran van Trung construction (left) for 5-(24,8,17) (# 5350) : der= 5-(24,7,3) and res= 5-(24,8,17) - the given design is the residual.

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# 5352: 5-(24,8,170)

• clan: 6-(25,8,30), 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5353: 5-(25,8,200)

• clan: 6-(25,8,30), 1 times reduced t
• Tran van Trung construction (left) for 5-(24,8,170) (# 5352) : der= 5-(24,7,30) and res= 5-(24,8,170) - the given design is the residual.

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# 5354: 5-(24,8,171)

• clan: 15-(32,16,3), 2 times reduced t, 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5355: 5-(24,8,172)

• clan: 5-(24,8,172)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5356: 5-(24,8,173)

• clan: 5-(24,8,173)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5357: 5-(24,8,174)

• clan: 13-(32,16,174), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5358: 5-(24,8,175)

• clan: 5-(24,8,175)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5359: 5-(24,8,176)

• clan: 5-(24,8,176)
• $PGL(2,23)$

---

# 5360: 5-(24,8,177)

• clan: 13-(32,16,177), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5361: 5-(24,8,178)

• clan: 5-(24,8,178)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5362: 5-(24,8,179)

• clan: 5-(24,8,179)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5363: 5-(24,8,18)

• clan: 13-(32,16,18), 8 times derived
• $PSL(2,23)$ 2 isomorphism types

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# 5364: 5-(24,8,180)

• clan: 13-(32,16,180), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• derived from 6-(25,9,180) (# 10420)

---

# 5365: 5-(24,8,181)

• clan: 5-(24,8,181)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5366: 5-(24,8,182)

• clan: 5-(24,8,182)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5367: 5-(24,8,183)

• clan: 13-(32,16,183), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5368: 5-(24,8,184)

• clan: 5-(24,8,184)
• $PGL(2,23)$

---

# 5369: 5-(24,8,185)

• clan: 5-(24,8,185)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5370: 5-(24,8,186)

• clan: 13-(32,16,186), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5371: 5-(24,8,187)

• clan: 6-(25,8,33), 1 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5372: 5-(25,8,220)

• clan: 6-(25,8,33), 1 times reduced t
• Tran van Trung construction (left) for 5-(24,8,187) (# 5371) : der= 5-(24,7,33) and res= 5-(24,8,187) - the given design is the residual.

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# 5373: 5-(24,8,188)

• clan: 5-(24,8,188)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5374: 5-(24,8,189)

• clan: 13-(32,16,189), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• derived from 6-(25,9,189) (# 10423)

---

# 5375: 5-(24,8,19)

• clan: 6-(24,8,3), 1 times reduced t
• $PSL(2,23)$ 1 isomorphism type

---

# 5376: 5-(24,8,190)

• clan: 6-(24,8,30), 1 times reduced t
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5377: 5-(24,8,191)

• clan: 5-(24,8,191)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5378: 5-(24,8,192)

• clan: 13-(32,16,192), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5379: 5-(24,8,193)

• clan: 5-(24,8,193)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5380: 5-(24,8,194)

• clan: 5-(24,8,194)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5381: 5-(24,8,195)

• clan: 13-(32,16,195), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5382: 5-(24,8,196)

• clan: 5-(24,8,196)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5383: 5-(24,8,197)

• clan: 5-(24,8,197)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5384: 5-(24,8,198)

• clan: 13-(32,16,198), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5385: 5-(24,8,199)

• clan: 5-(24,8,199)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5386: 5-(24,8,2)

• clan: 5-(24,8,2)
• \cite{KramerMagliveras74}
• \cite{AssmusMattson66a} $PGL(2,23))$

---

# 5387: 5-(24,8,20)

• clan: 5-(24,8,20)
• $PSL(2,23)$ 3 isomorphism types

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# 5388: 5-(24,8,200)

• clan: 5-(24,8,200)
• $PGL(2,23)$

---

# 5389: 5-(24,8,201)

• clan: 13-(32,16,201), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5390: 5-(24,8,202)

• clan: 5-(24,8,202)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5391: 5-(24,8,203)

• clan: 5-(24,8,203)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5392: 5-(24,8,204)

• clan: 17-(36,18,4), 10 times derived, 2 times residual
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23
• residual design of 6-(25,8,36) (# 10396)
• derived from 6-(25,9,204) (# 10426)

---

# 5393: 5-(25,8,240)

• clan: 17-(36,18,4), 1 times reduced t, 10 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(24,8,204) (# 5392) : der= 5-(24,7,36) and res= 5-(24,8,204) - the given design is the residual.
• design 6-(25,8,36) (# 10396) with respect to smaller t
• derived from 6-(26,9,240) (# 10429)
• derived from supplementary of 6-(26,9,900) (# 13788)

---

# 5394: 5-(26,8,280)

• clan: 17-(36,18,4), 2 times reduced t, 10 times derived
• Tran van Trung construction (left) for 5-(25,8,240) (# 5393) : der= 5-(25,7,40) and res= 5-(25,8,240) - the given design is the residual.
• derived from 6-(27,9,280) (# 11614)

---

# 5395: 5-(24,8,205)

• clan: 5-(24,8,205)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5396: 5-(24,8,206)

• clan: 5-(24,8,206)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5397: 5-(24,8,207)

• clan: 13-(32,16,207), 8 times derived
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5398: 5-(24,8,208)

• clan: 5-(24,8,208)
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

# 5399: 5-(24,8,209)

• clan: 6-(24,8,33), 1 times reduced t
• $ {\bf PSL(2,23)} \geq 1$ % -group 3 PSL 2 23 PSL_2_23

---

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created: Fri Oct 23 11:10:08 CEST 2009