t designs with small t, id ge 300

---

# 300: 5-(22,11,6160)

• clan: 7-(24,12,3080), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6160) (# 299)
• residual design of 6-(23,11,3080) (# 9704)
• derived from 6-(23,12,6160) (# 9714)
• residual design of supplementary of 6-(23,11,3108) (# 9716)
• derived from supplementary of 6-(23,12,6216) (# 9717)

---

# 301: 4-(21,10,6188)

• clan: 14-(30,15,8), 1 times reduced t, 5 times derived, 4 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 302: 5-(22,11,6188)

• clan: 14-(30,15,8), 1 times reduced t, 4 times derived, 4 times residual
• Alltop construction for design 4-(21,10,6188) (# 301)
• Tran van Trung construction with complementary design for 5-(21,10,2184) (# 955)
• Tran van Trung construction (right) for 5-(21,10,2184) (# 955) : der= 5-(21,10,2184) and res= 5-(21,11,4004) - the given design is the derived.
• design 6-(22,11,2184) (# 956) with respect to smaller t
• supplementary design of 6-(22,11,2184) (# 956) with respect to smaller t
• Tran van Trung construction (left) for 5-(21,11,4004) (# 957) : der= 5-(21,10,2184) and res= 5-(21,11,4004) - the given design is the residual.

---

# 303: 4-(21,10,6216)

• clan: 7-(24,12,3108), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 304: 5-(22,11,6216)

• clan: 7-(24,12,3108), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6216) (# 303)
• residual design of supplementary of 6-(23,11,3080) (# 9704)
• derived from supplementary of 6-(23,12,6160) (# 9714)
• residual design of 6-(23,11,3108) (# 9716)
• derived from 6-(23,12,6216) (# 9717)

---

# 305: 4-(21,10,6244)

• clan: 7-(24,12,3122), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 306: 5-(22,11,6244)

• clan: 7-(24,12,3122), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6244) (# 305)

---

# 307: 4-(21,10,6272)

• clan: 7-(24,12,3136), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 308: 5-(22,11,6272)

• clan: 7-(24,12,3136), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6272) (# 307)

---

# 309: 4-(21,10,6300)

• clan: 7-(24,12,3150), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 310: 5-(22,11,6300)

• clan: 7-(24,12,3150), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6300) (# 309)
• residual design of supplementary of 6-(23,11,3038) (# 9687)
• derived from supplementary of 6-(23,12,6076) (# 9697)
• residual design of 6-(23,11,3150) (# 9699)
• derived from 6-(23,12,6300) (# 9700)

---

# 311: 4-(21,10,6328)

• clan: 7-(24,12,3164), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 312: 5-(22,11,6328)

• clan: 7-(24,12,3164), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6328) (# 311)
• $PSL(3,4)+$

---

# 313: 4-(21,10,6356)

• clan: 7-(24,12,3178), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 314: 5-(22,11,6356)

• clan: 7-(24,12,3178), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6356) (# 313)

---

# 315: 4-(21,10,6384)

• clan: 7-(24,12,3192), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 316: 5-(22,11,6384)

• clan: 7-(24,12,3192), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6384) (# 315)
• $PSL(3,4)+$

---

# 317: 4-(21,10,6412)

• clan: 7-(24,12,3206), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 318: 5-(22,11,6412)

• clan: 7-(24,12,3206), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6412) (# 317)
• residual design of supplementary of 6-(23,11,2982) (# 9670)
• derived from supplementary of 6-(23,12,5964) (# 9680)
• residual design of 6-(23,11,3206) (# 9682)
• derived from 6-(23,12,6412) (# 9683)

---

# 319: 4-(21,10,6496)

• clan: 7-(24,12,3248), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 320: 5-(22,11,6496)

• clan: 7-(24,12,3248), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6496) (# 319)

---

# 321: 4-(21,10,6552)

• clan: 15-(32,16,9), 6 times derived, 5 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 322: 5-(22,11,6552)

• clan: 15-(32,16,9), 5 times derived, 5 times residual
• Alltop construction for design 4-(21,10,6552) (# 321)
• $PSL(3,4)+$
• residual design of supplementary of 6-(23,11,2912) (# 9645)
• derived from supplementary of 6-(23,12,5824) (# 9652)
• residual design of 6-(23,11,3276) (# 9654)
• derived from 6-(23,12,6552) (# 9655)

---

# 323: 4-(21,10,6580)

• clan: 7-(24,12,3290), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 324: 5-(22,11,6580)

• clan: 7-(24,12,3290), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6580) (# 323)
• residual design of supplementary of 6-(23,11,2898) (# 9630)
• derived from supplementary of 6-(23,12,5796) (# 9638)
• residual design of 6-(23,11,3290) (# 9640)
• derived from 6-(23,12,6580) (# 9641)

---

# 325: 4-(21,10,6636)

• clan: 7-(24,12,3318), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 326: 5-(22,11,6636)

• clan: 7-(24,12,3318), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6636) (# 325)

---

# 327: 4-(21,10,6664)

• clan: 11-(24,12,7), 4 times reduced t, 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 328: 5-(22,11,6664)

• clan: 11-(24,12,7), 4 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6664) (# 327)
• Tran van Trung construction with complementary design for 5-(21,10,2352) (# 958)
• Tran van Trung construction (right) for 5-(21,10,2352) (# 958) : der= 5-(21,10,2352) and res= 5-(21,11,4312) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,11,4312) (# 959) : der= 5-(21,10,2352) and res= 5-(21,11,4312) - the given design is the residual.
• supplementary design of 6-(22,11,2016) (# 8713) with respect to smaller t
• residual design of supplementary of 6-(23,11,2856) (# 8714)
• derived from supplementary of 6-(23,12,5712) (# 8719)
• residual design of 6-(23,11,3332) (# 8721)
• derived from 6-(23,12,6664) (# 8722)
• design 6-(22,11,2352) (# 13140) with respect to smaller t

---

# 329: 4-(21,10,672)

• clan: 7-(24,12,336), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+
• PSL(3,4)

---

# 330: 5-(22,11,672)

• clan: 7-(24,12,336), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,672) (# 329)
• $PSL(3,4)+$ 9 isomorphism types, Alltop construction from 4-(21,10,672)
• \cite{Kreher95} $PGL(2,19)++$ 1 isomorphism type

---

# 331: 4-(21,10,6720)

• clan: 7-(24,12,3360), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 332: 5-(22,11,6720)

• clan: 7-(24,12,3360), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6720) (# 331)

---

# 333: 4-(21,10,6804)

• clan: 7-(24,12,3402), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 334: 5-(22,11,6804)

• clan: 7-(24,12,3402), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6804) (# 333)
• residual design of supplementary of 6-(23,11,2786) (# 9613)
• derived from supplementary of 6-(23,12,5572) (# 9623)
• residual design of 6-(23,11,3402) (# 9625)
• derived from 6-(23,12,6804) (# 9626)

---

# 335: 4-(21,10,6832)

• clan: 7-(24,12,3416), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 336: 5-(22,11,6832)

• clan: 7-(24,12,3416), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,6832) (# 335)
• $PSL(3,4)+$
• residual design of supplementary of 6-(23,11,2772) (# 9598)
• derived from supplementary of 6-(23,12,5544) (# 9606)
• residual design of 6-(23,11,3416) (# 9608)
• derived from 6-(23,12,6832) (# 9609)

---

# 337: 4-(21,10,700)

• clan: 7-(24,12,350), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 338: 5-(22,11,700)

• clan: 7-(24,12,350), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,700) (# 337)

---

# 339: 4-(21,10,756)

• clan: 7-(24,12,378), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 340: 5-(22,11,756)

• clan: 7-(24,12,378), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,756) (# 339)

---

# 341: 4-(21,10,784)

• clan: 7-(24,12,392), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 342: 5-(22,11,784)

• clan: 7-(24,12,392), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,784) (# 341)

---

# 343: 4-(21,10,840)

• clan: 7-(24,12,420), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 344: 5-(22,11,840)

• clan: 7-(24,12,420), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,840) (# 343)
• $PGL(2,19)++$

---

# 345: 4-(21,10,924)

• clan: 7-(24,12,462), 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 346: 5-(22,11,924)

• clan: 7-(24,12,462), 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,924) (# 345)

---

# 347: 4-(21,10,952)

• clan: 11-(24,12,1), 4 times reduced t, 2 times derived, 1 times residual
• $ {\bf PSL(2,19)}^+ $ % -group 4 PSL 2 19 Add_fixpoint PSL_2_19+

---

# 348: 5-(22,11,952)

• clan: 11-(24,12,1), 4 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 4-(21,10,952) (# 347)
• Tran van Trung construction with complementary design for 5-(21,10,336) (# 946)
• Tran van Trung construction (right) for 5-(21,10,336) (# 946) : der= 5-(21,10,336) and res= 5-(21,11,616) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,11,616) (# 948) : der= 5-(21,10,336) and res= 5-(21,11,616) - the given design is the residual.
• $PGL(2,19)++$ 439 solutions
• $PSL(3,4)+$ 9 isomorphism types
• \cite{Kreher95}

---

# 349: 4-(21,5,2)

• clan: 15-(32,16,2), 11 times derived
• $Hol(C_7)\times C_3$ 46 solutions

---

# 350: 4-(21,5,3)

• clan: 15-(32,16,3), 11 times derived
• $Hol(C_{21})$ 3 solutions

---

# 351: 4-(21,5,4)

• clan: 15-(32,16,4), 11 times derived
• $PGL(3,2)^{[2]}$

---

# 352: 4-(21,5,5)

• clan: 15-(32,16,5), 11 times derived
• $Hol(C_{21})$ 49 solutions
• $PGL(3,2)^{[2]}$

---

# 353: 4-(21,5,6)

• clan: 15-(32,16,6), 11 times derived
• $Hol(C_{19})++$ 35522 solutions
• $Hol(C_{21})$

---

# 354: 4-(21,5,8)

• clan: 15-(32,16,8), 11 times derived
• $Hol(C_{19})++$
• $Hol(C_{21})$
• $PGL(3,2)^{[2]}$

---

# 355: 4-(21,6,10)

• clan: 5-(22,7,10), 1 times derived
• $Hol(C_{21})$

---

# 356: 4-(21,6,12)

• clan: 13-(30,15,12), 9 times derived
• $Hol(C_{21})$

---

# 357: 4-(21,6,16)

• clan: 15-(32,16,2), 10 times derived, 1 times residual
• $Hol(C_{21})$

---

# 358: 4-(21,6,18)

• clan: 5-(22,7,18), 1 times derived
• $Hol(C_{21})$

---

# 359: 4-(21,6,22)

• clan: 5-(22,7,22), 1 times derived
• $Hol(C_{21})$ many solutions

---

# 360: 4-(21,6,24)

• clan: 15-(32,16,3), 10 times derived, 1 times residual
• $Hol(C_{21})$ many solutions, $PGL(3,2)\times C_3$

---

# 361: 4-(21,6,28)

• clan: 13-(30,15,28), 9 times derived
• $Hol(C_{21})$ many solutions

---

# 362: 4-(21,6,30)

• clan: 5-(22,7,30), 1 times derived
• $Hol(C_{21})$ many solutions

---

# 363: 4-(21,6,34)

• clan: 6-(22,7,4), 1 times reduced t, 1 times derived
• $Hol(C_{21})$ many solutions

---

# 364: 4-(21,6,36)

• clan: 13-(30,15,36), 9 times derived
• $Hol(C_{21})$ many solutions

---

# 365: 4-(21,6,40)

• clan: 15-(32,16,5), 10 times derived, 1 times residual
• $Hol(C_{21})$ many solutions

---

# 366: 4-(21,6,42)

• clan: 5-(22,7,42), 1 times derived
• $Hol(C_{21})$ many solutions

---

# 367: 4-(21,6,46)

• clan: 5-(22,7,46), 1 times derived
• $Hol(C_{21})$ many solutions

---

# 368: 4-(21,6,54)

• clan: 5-(22,7,54), 1 times derived
• $Hol(C_{21})$

---

# 369: 4-(21,6,60)

• clan: 13-(30,15,60), 9 times derived
• $A_7^{[2]}$ 2 solutions, $Hol(C_{21})$ many solutions

---

# 370: 4-(21,6,64)

• clan: 15-(32,16,8), 10 times derived, 1 times residual
• $Hol(C_{21})$ many solutions

---

# 371: 4-(21,6,66)

• clan: 5-(22,7,66), 1 times derived
• $Hol(C_{21})$ many solutions

---

# 372: 4-(21,9,1820)

• clan: 15-(32,16,5), 7 times derived, 4 times residual
• $PSL(3,4)$

---

# 373: 4-(21,9,2156)

• clan: 7-(24,12,2156), 3 times derived
• $PSL(3,4)$

---

# 374: 4-(21,9,2688)

• clan: 7-(24,12,2688), 3 times derived
• $PSL(3,4)$

---

# 375: 4-(21,9,3024)

• clan: 7-(24,12,3024), 3 times derived
• $PSL(3,4)$

---

# 376: 4-(21,9,3164)

• clan: 7-(24,12,3164), 3 times derived
• $PSL(3,4)$

---

# 377: 4-(21,9,4032)

• clan: 7-(24,12,4032), 3 times derived
• $PSL(3,4)$

---

# 378: 4-(22,6,24)

• clan: 6-(24,8,24), 2 times derived
• $PSL(2,11)$ 13 solutions

---

# 379: 4-(22,6,27)

• clan: 15-(32,16,3), 1 times reduced t, 10 times derived
• $PSL(2,11)$ 69 solutions

---

# 380: 4-(22,6,36)

• clan: 15-(32,16,4), 1 times reduced t, 10 times derived
• $PSL(2,11)$ 3907 solutions

---

# 381: 4-(22,6,39)

• clan: 6-(24,8,39), 2 times derived
• $PSL(2,11)$ 7847 solutions

---

# 382: 4-(22,6,42)

• clan: 6-(24,8,42), 2 times derived
• $PSL(2,11)$ 21731 solutions

---

# 383: 4-(22,6,45)

• clan: 15-(32,16,5), 1 times reduced t, 10 times derived
• $PSL(2,11)$ 9989 solutions

---

# 384: 4-(22,6,48)

• clan: 6-(24,8,48), 2 times derived
• $PSL(2,11)$ 60011 solutions

---

# 385: 4-(22,6,54)

• clan: 15-(32,16,6), 1 times reduced t, 10 times derived
• $PSL(2,11)$ 1226940 solutions

---

# 386: 4-(22,6,57)

• clan: 6-(24,8,57), 2 times derived
• $PSL(2,11)$

---

# 387: 4-(22,6,63)

• clan: 15-(32,16,7), 1 times reduced t, 10 times derived
• $PSL(2,11)$

---

# 388: 4-(22,6,66)

• clan: 6-(24,8,66), 2 times derived
• $PSL(2,11)$

---

# 389: 4-(22,6,72)

• clan: 15-(32,16,8), 1 times reduced t, 10 times derived
• $PSL(2,11)$

---

# 390: 4-(25,6,30)

• clan: 5-(26,6,3), 1 times residual
• \cite{KreherTechReport95}

---

# 391: 4-(25,6,60)

• clan: 5-(26,6,6), 1 times residual
• \cite{KreherTechReport95}

---

# 392: 4-(25,7,140)

• clan: 17-(36,18,2), 2 times reduced t, 11 times derived
• \cite{KreherTechReport95}

---

# 393: 4-(25,7,210)

• clan: 17-(36,18,3), 2 times reduced t, 11 times derived
• \cite{KreherTechReport95}

---

# 394: 4-(26,5,10)

• clan: 9-(31,10,10), 5 times derived
• $Hol(C_{26})$ many isomorphism types

---

# 395: 4-(26,5,12)

• clan: 9-(31,10,12), 5 times derived
• $Hol(C_{26})$ many isomorphism types

---

# 396: 4-(26,5,4)

• clan: 9-(31,10,4), 5 times derived
• $Hol(C_{26})$ many isomorphism types

---

# 397: 4-(30,5,8)

• clan: 11-(37,12,8), 7 times derived
• \cite{Kreher95}

---

# 398: 4-(30,6,15)

• clan: 10-(36,12,15), 6 times derived
• \cite{Kreher95}

---

# 399: 4-(33,8,10500)

• clan: 8-(37,12,10500), 4 times derived
• $M_{11}\times C_3$

---

---

created: Fri Oct 23 11:09:29 CEST 2009