t designs with small t, id ge 400
# 400: 4-(33,8,9828)
# 401: 4-(52,5,24)
# 402: 4-(56,5,12)
# 403: 4-(56,5,16)
# 404: 4-(56,5,24)
# 405: 4-(57,6,196)
# 406: 4-(57,7,294)
# 407: 4-(66,6,60)
# 408: 4-(66,6,151)
# 409: 4-(66,6,360)
# 410: 4-(66,6,420)
# 411: 4-(81,5,5)
# 412: 4-(81,5,36)
# 413: 4-(81,6,36)
# 414: 5-(108,6,1)
# 415: 5-(13,6,4)
# 416: 5-(14,7,18)
- clan: 6-(14,7,4), 1 times reduced t
-
Tran van Trung construction with complementary design for 5-(13,6,4) (# 415)
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Tran van Trung construction (right) for 5-(13,6,4) (# 415) : der= 5-(13,6,4) and res= 5-(13,7,14) - the given design is the derived.
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design 6-(14,7,4) (# 417) with respect to smaller t
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supplementary design of 6-(14,7,4) (# 417) with respect to smaller t
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Tran van Trung construction (left) for 5-(13,7,14) (# 418) : der= 5-(13,6,4) and res= 5-(13,7,14) - the given design is the residual.
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$LS[2](5,7,14)$ $C_{13}+$
# 417: 6-(14,7,4)
- clan: 6-(14,7,4)
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Alltop construction for design 5-(13,6,4) (# 415)
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$A_4$ (1 isom. type) \cite{LBH2001}
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$C_3$ (4 isom. types) \cite{EslamiKhosrovshahi2001}
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$C_7$ (2 isom. types) \cite{KhosrovshahiMohammadNooriTayfehRezaie2001}
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$C_2$ (4 isom. types) \cite{KhosrovshahiMohammadNooriTayfehRezaie2001}
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$C_{13}+$ (2 isom. types) \cite{KreherRadziszowski86}, Halving of the complete design
# 418: 5-(13,7,14)
# 419: 5-(132,6,1)
# 420: 5-(14,6,3)
# 421: 5-(14,7,12)
# 422: 5-(15,7,15)
- clan: 7-(16,8,3), 1 times reduced t, 1 times derived
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Tran van Trung construction (left) for 5-(14,7,12) (# 421) : der= 5-(14,6,3) and res= 5-(14,7,12) - the given design is the residual.
# 423: 5-(15,8,40)
# 424: 5-(16,6,3)
- clan: 9-(20,10,3), 4 times derived
-
Brouwer 1977/1986
-
$D_8\times C_2$ >= 86 solutions
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$PSL(2,7)\times Id_2$ 3 solutions
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$PSL(2,7)\times C_2$ 1 solution
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$PGL(2,7)\times C_2$ 1 solution
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$PGL(2,7) twist C_2$ 3 solutions
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$PGL(2,7)\times Id_2$ 1 solution
# 425: 5-(16,6,4)
# 426: 5-(16,6,5)
- clan: 9-(20,10,5), 4 times derived
-
Brouwer 1977/1986
-
$PSL(2,7)\times Id_2$ 12 solutions
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$PSL(2,7)\times C_2$ 4 solutions
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$PGL(2,7) twist C_2$ 4 solutions
# 427: 5-(16,7,15)
# 428: 5-(17,7,18)
- clan: 9-(20,10,3), 1 times reduced t, 3 times derived
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Tran van Trung construction (left) for 5-(16,7,15) (# 427) : der= 5-(16,6,3) and res= 5-(16,7,15) - the given design is the residual.
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$(A_4\times D_4)+$ (many isom. types)
# 429: 5-(17,8,60)
- clan: 9-(20,10,3), 1 times reduced t, 2 times derived, 1 times residual
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Tran van Trung construction (right) for 5-(16,7,15) (# 427) : der= 5-(16,7,15) and res= 5-(16,8,45) - the given design is the derived.
# 430: 5-(18,8,78)
- clan: 9-(20,10,3), 2 times reduced t, 2 times derived
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Tran van Trung construction (right) for 5-(17,7,18) (# 428) : der= 5-(17,7,18) and res= 5-(17,8,60) - the given design is the derived.
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Tran van Trung construction (left) for 5-(17,8,60) (# 429) : der= 5-(17,7,18) and res= 5-(17,8,60) - the given design is the residual.
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\cite{Kramer75} $PGL(2,17)$ 8 isomorphism types TvT: 5-(17,7,18) $\cup$ 5-(17,8,60) \cite{TranvanTrung86}
# 431: 5-(18,9,195)
- clan: 9-(20,10,3), 2 times reduced t, 1 times derived, 1 times residual
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Tran van Trung construction with complementary design for 5-(17,8,60) (# 429)
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Tran van Trung construction (right) for 5-(17,8,60) (# 429) : der= 5-(17,8,60) and res= 5-(17,9,135) - the given design is the derived.
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Tran van Trung construction (left) for 5-(17,9,135) (# 432) : der= 5-(17,8,60) and res= 5-(17,9,135) - the given design is the residual.
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\cite{Brouwer86} Alltop(res(5-(18,8,78))
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\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type
# 432: 5-(17,9,135)
# 433: 5-(19,9,273)
- clan: 9-(20,10,3), 3 times reduced t, 1 times derived
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Tran van Trung construction (right) for 5-(18,8,78) (# 430) : der= 5-(18,8,78) and res= 5-(18,9,195) - the given design is the derived.
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Tran van Trung construction (left) for 5-(18,9,195) (# 431) : der= 5-(18,8,78) and res= 5-(18,9,195) - the given design is the residual.
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$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
# 434: 5-(20,10,819)
- clan: 9-(20,10,3), 4 times reduced t
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Tran van Trung construction with complementary design for 5-(19,9,273) (# 433)
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Tran van Trung construction (right) for 5-(19,9,273) (# 433) : der= 5-(19,9,273) and res= 5-(19,10,546) - the given design is the derived.
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Tran van Trung construction (left) for 5-(19,10,546) (# 435) : der= 5-(19,9,273) and res= 5-(19,10,546) - the given design is the residual.
-
\cite{Krameretal85}
-
\cite{TranvanTrung86}
# 435: 5-(19,10,546)
# 436: 5-(16,7,20)
# 437: 5-(17,7,24)
- clan: 9-(20,10,4), 1 times reduced t, 3 times derived
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Tran van Trung construction (left) for 5-(16,7,20) (# 436) : der= 5-(16,6,4) and res= 5-(16,7,20) - the given design is the residual.
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Brouwer 1977/1986 $Hol(C_{17})$
# 438: 5-(17,8,80)
- clan: 9-(20,10,4), 1 times reduced t, 2 times derived, 1 times residual
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Tran van Trung construction (right) for 5-(16,7,20) (# 436) : der= 5-(16,7,20) and res= 5-(16,8,60) - the given design is the derived.
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\cite{Kramer75} $PGL(2,16)$
# 439: 5-(18,8,104)
- clan: 9-(20,10,4), 2 times reduced t, 2 times derived
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Tran van Trung construction (right) for 5-(17,7,24) (# 437) : der= 5-(17,7,24) and res= 5-(17,8,80) - the given design is the derived.
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Tran van Trung construction (left) for 5-(17,8,80) (# 438) : der= 5-(17,7,24) and res= 5-(17,8,80) - the given design is the residual.
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$C_2\times PGL(2,8)$
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\cite{Kramer75}
# 440: 5-(18,9,260)
- clan: 9-(20,10,4), 2 times reduced t, 1 times derived, 1 times residual
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Tran van Trung construction with complementary design for 5-(17,8,80) (# 438)
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Tran van Trung construction (right) for 5-(17,8,80) (# 438) : der= 5-(17,8,80) and res= 5-(17,9,180) - the given design is the derived.
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Tran van Trung construction (left) for 5-(17,9,180) (# 441) : der= 5-(17,8,80) and res= 5-(17,9,180) - the given design is the residual.
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\cite{Brouwer86} $Hol(C_17)+$
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\cite{Brouwer86} Alltop(res(5-(18,8,104))
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\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
# 441: 5-(17,9,180)
# 442: 5-(19,9,364)
- clan: 9-(20,10,4), 3 times reduced t, 1 times derived
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Tran van Trung construction (right) for 5-(18,8,104) (# 439) : der= 5-(18,8,104) and res= 5-(18,9,260) - the given design is the derived.
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Tran van Trung construction (left) for 5-(18,9,260) (# 440) : der= 5-(18,8,104) and res= 5-(18,9,260) - the given design is the residual.
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$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
# 443: 5-(20,10,1092)
- clan: 9-(20,10,4), 4 times reduced t
-
Tran van Trung construction with complementary design for 5-(19,9,364) (# 442)
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Tran van Trung construction (right) for 5-(19,9,364) (# 442) : der= 5-(19,9,364) and res= 5-(19,10,728) - the given design is the derived.
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Tran van Trung construction (left) for 5-(19,10,728) (# 444) : der= 5-(19,9,364) and res= 5-(19,10,728) - the given design is the residual.
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\cite{Krameretal85} $PSL(2,19)$
# 444: 5-(19,10,728)
# 445: 5-(16,7,25)
# 446: 5-(17,7,30)
- clan: 9-(20,10,5), 1 times reduced t, 3 times derived
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Tran van Trung construction (left) for 5-(16,7,25) (# 445) : der= 5-(16,6,5) and res= 5-(16,7,25) - the given design is the residual.
# 447: 5-(17,8,100)
- clan: 9-(20,10,5), 1 times reduced t, 2 times derived, 1 times residual
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Tran van Trung construction (right) for 5-(16,7,25) (# 445) : der= 5-(16,7,25) and res= 5-(16,8,75) - the given design is the derived.
# 448: 5-(18,8,130)
- clan: 9-(20,10,5), 2 times reduced t, 2 times derived
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Tran van Trung construction (right) for 5-(17,7,30) (# 446) : der= 5-(17,7,30) and res= 5-(17,8,100) - the given design is the derived.
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Tran van Trung construction (left) for 5-(17,8,100) (# 447) : der= 5-(17,7,30) and res= 5-(17,8,100) - the given design is the residual.
-
\cite{Kramer75} $PGL(2,17)$ 11 isomorphism types
# 449: 5-(18,9,325)
- clan: 9-(20,10,5), 2 times reduced t, 1 times derived, 1 times residual
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Tran van Trung construction with complementary design for 5-(17,8,100) (# 447)
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Tran van Trung construction (right) for 5-(17,8,100) (# 447) : der= 5-(17,8,100) and res= 5-(17,9,225) - the given design is the derived.
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Tran van Trung construction (left) for 5-(17,9,225) (# 450) : der= 5-(17,8,100) and res= 5-(17,9,225) - the given design is the residual.
-
$Ico\times Octa$ 13216 solutions
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\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types
# 450: 5-(17,9,225)
# 451: 5-(19,9,455)
- clan: 9-(20,10,5), 3 times reduced t, 1 times derived
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Tran van Trung construction (right) for 5-(18,8,130) (# 448) : der= 5-(18,8,130) and res= 5-(18,9,325) - the given design is the derived.
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Tran van Trung construction (left) for 5-(18,9,325) (# 449) : der= 5-(18,8,130) and res= 5-(18,9,325) - the given design is the residual.
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$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
# 452: 5-(20,10,1365)
- clan: 9-(20,10,5), 4 times reduced t
-
Tran van Trung construction with complementary design for 5-(19,9,455) (# 451)
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Tran van Trung construction (right) for 5-(19,9,455) (# 451) : der= 5-(19,9,455) and res= 5-(19,10,910) - the given design is the derived.
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Tran van Trung construction (left) for 5-(19,10,910) (# 453) : der= 5-(19,9,455) and res= 5-(19,10,910) - the given design is the residual.
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\cite{Krameretal85} $PGL(2,19)$
-
\cite{TranvanTrung86}
# 453: 5-(19,10,910)
# 454: 5-(168,6,1)
# 455: 5-(17,7,12)
# 456: 5-(17,7,36)
# 457: 5-(18,6,4)
# 458: 5-(18,6,5)
# 459: 5-(18,7,12)
# 460: 5-(18,7,18)
# 461: 5-(18,7,24)
# 462: 5-(19,7,28)
- clan: 11-(24,12,4), 1 times reduced t, 5 times derived
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Tran van Trung construction (left) for 5-(18,7,24) (# 461) : der= 5-(18,6,4) and res= 5-(18,7,24) - the given design is the residual.
-
$Hol(C_{19})$ (>=1 isom. types)
-
Brouwer 1977/1986
-
design 6-(19,7,4) (# 8609) with respect to smaller t
-
derived from 6-(20,8,28) (# 8658)
# 463: 5-(18,7,30)
# 464: 5-(19,7,35)
- clan: 11-(24,12,5), 1 times reduced t, 5 times derived
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Tran van Trung construction (left) for 5-(18,7,30) (# 463) : der= 5-(18,6,5) and res= 5-(18,7,30) - the given design is the residual.
-
Brouwer 1977/1986
# 465: 5-(18,7,36)
# 466: 5-(18,7,6)
# 467: 5-(18,8,102)
# 468: 5-(18,8,108)
# 469: 5-(18,8,110)
# 470: 5-(19,8,140)
- clan: 11-(24,12,5), 1 times reduced t, 4 times derived, 1 times residual
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Tran van Trung construction (left) for 5-(18,8,110) (# 469) : der= 5-(18,7,30) and res= 5-(18,8,110) - the given design is the residual.
# 471: 5-(20,8,175)
- clan: 11-(24,12,5), 2 times reduced t, 4 times derived
-
Tran van Trung construction (left) for 5-(19,8,140) (# 470) : der= 5-(19,7,35) and res= 5-(19,8,140) - the given design is the residual.
-
\cite{Krameretal85} $PGL(2,19)$ 343 isomorphism types
# 472: 5-(18,8,112)
# 473: 5-(18,8,114)
# 474: 5-(18,8,118)
# 475: 5-(18,8,120)
# 476: 5-(18,8,122)
# 477: 5-(18,8,124)
# 478: 5-(18,8,126)
- clan: 7-(20,10,126), 2 times derived
-
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types
-
$C_2\times PGL(2,8)$
-
$PSL(2,8)\times C_2$ (many solutions)
-
derived from 6-(19,9,126) (# 8643)
-
derived from supplementary of 6-(19,9,160) (# 8650)
# 479: 5-(18,8,128)
# 480: 5-(18,8,132)
# 481: 5-(19,8,168)
- clan: 11-(24,12,6), 1 times reduced t, 4 times derived, 1 times residual
-
Tran van Trung construction (left) for 5-(18,8,132) (# 480) : der= 5-(18,7,36) and res= 5-(18,8,132) - the given design is the residual.
# 482: 5-(18,8,136)
# 483: 5-(18,8,138)
# 484: 5-(18,8,14)
# 485: 5-(18,8,140)
# 486: 5-(18,8,142)
# 487: 5-(18,8,16)
# 488: 5-(18,8,30)
# 489: 5-(18,8,32)
# 490: 5-(18,8,36)
# 491: 5-(18,8,38)
# 492: 5-(18,8,40)
# 493: 5-(18,8,42)
# 494: 5-(18,8,44)
# 495: 5-(19,8,56)
- clan: 11-(24,12,2), 1 times reduced t, 4 times derived, 1 times residual
-
Tran van Trung construction (left) for 5-(18,8,44) (# 494) : der= 5-(18,7,12) and res= 5-(18,8,44) - the given design is the residual.
# 496: 5-(18,8,46)
- clan: 7-(20,10,46), 2 times derived
-
$C_2\times ASL(2,3)$ 24 solutions
-
\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types $PGL(2,16)+$ 1 isomorphism type
# 497: 5-(18,8,48)
- clan: 7-(20,10,48), 2 times derived
-
$C_2\times ASL(2,3)$ 858 solutions
-
$C_2\times PGL(2,8)$ 465 solutions
-
\cite{Kramer75} $PGL(2,17)$ 5 isomorphism types
# 498: 5-(18,8,50)
# 499: 5-(18,8,52)
created: Fri Oct 23 11:09:31 CEST 2009