t designs with small t, id ge 400

clan: 6-(14,7,4), 1 times reduced t
Tran van Trung construction with complementary design for 5-(13,6,4) (# 415)
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.
design 6-(14,7,4) (# 417) with respect to smaller t
supplementary design of 6-(14,7,4) (# 417) with respect to smaller t
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.
$LS[2](5,7,14)$ $C_{13}+$

# 417: 6-(14,7,4)

clan: 6-(14,7,4)
Alltop construction for design 5-(13,6,4) (# 415)
$A_4$ (1 isom. type) \cite{LBH2001}
$C_3$ (4 isom. types) \cite{EslamiKhosrovshahi2001}
$C_7$ (2 isom. types) \cite{KhosrovshahiMohammadNooriTayfehRezaie2001}
$C_2$ (4 isom. types) \cite{KhosrovshahiMohammadNooriTayfehRezaie2001}
$C_{13}+$ (2 isom. types) \cite{KreherRadziszowski86}, Halving of the complete design

# 418: 5-(13,7,14)

clan: 6-(14,7,4), 1 times residual
complementary design of 5-(13,6,4) (# 415)
residual design of 6-(14,7,4) (# 417)
residual design of supplementary of 6-(14,7,4) (# 417)

# 419: 5-(132,6,1)

clan: 125-(252,126,1), 120 times derived
$PSL(2,131)$ \cite{GrannellGriggsMathon} >= 100 isomorphism types

# 420: 5-(14,6,3)

clan: 7-(16,8,3), 2 times derived
$C_{13}C_3+$ 1 isomorphism type Brouwer 1977/1986

# 421: 5-(14,7,12)

clan: 7-(16,8,3), 1 times derived, 1 times residual
$C_4xId_3$ (halving of the complete design),
$LS[3](5,7,14)$ Alltop-extension $LS[3](4,6,13)$

# 422: 5-(15,7,15)

clan: 7-(16,8,3), 1 times reduced t, 1 times derived
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)

clan: 7-(16,8,3), 1 times reduced t, 1 times residual
complementary design of 5-(15,7,15) (# 422)

# 424: 5-(16,6,3)

clan: 9-(20,10,3), 4 times derived
Brouwer 1977/1986
$D_8\times C_2$ >= 86 solutions
$PSL(2,7)\times Id_2$ 3 solutions
$PSL(2,7)\times C_2$ 1 solution
$PGL(2,7)\times C_2$ 1 solution
$PGL(2,7) twist C_2$ 3 solutions
$PGL(2,7)\times Id_2$ 1 solution

# 425: 5-(16,6,4)

clan: 9-(20,10,4), 4 times derived
$D_8\times C_2$
$D_{16}$

# 426: 5-(16,6,5)

clan: 9-(20,10,5), 4 times derived
Brouwer 1977/1986
$PSL(2,7)\times Id_2$ 12 solutions
$PSL(2,7)\times C_2$ 4 solutions
$PGL(2,7) twist C_2$ 4 solutions

# 427: 5-(16,7,15)

clan: 9-(20,10,3), 3 times derived, 1 times residual
$A_4\times D_4$ 42 solutions
$Hol(C_8)\times C_2$ 56 solutions
Brouwer 1977/1986

# 428: 5-(17,7,18)

clan: 9-(20,10,3), 1 times reduced t, 3 times derived
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.
$(A_4\times D_4)+$ (many isom. types)

# 429: 5-(17,8,60)

clan: 9-(20,10,3), 1 times reduced t, 2 times derived, 1 times residual
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
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.
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.
\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
Tran van Trung construction with complementary design for 5-(17,8,60) (# 429)
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.
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.
\cite{Brouwer86} Alltop(res(5-(18,8,78))
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

# 432: 5-(17,9,135)

clan: 9-(20,10,3), 1 times reduced t, 1 times derived, 2 times residual
complementary design of 5-(17,8,60) (# 429)

# 433: 5-(19,9,273)

clan: 9-(20,10,3), 3 times reduced t, 1 times derived
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.
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.
$ {\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
Tran van Trung construction with complementary design for 5-(19,9,273) (# 433)
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.
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)

clan: 9-(20,10,3), 3 times reduced t, 1 times residual
complementary design of 5-(19,9,273) (# 433)

# 436: 5-(16,7,20)

clan: 9-(20,10,4), 3 times derived, 1 times residual
$Hol(C_8)\times C_2$ 126784 solutions
$D_4\times D_4$
$HoL(C_{16})$ Wassermann 152 solutions

# 437: 5-(17,7,24)

clan: 9-(20,10,4), 1 times reduced t, 3 times derived
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.
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
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.
\cite{Kramer75} $PGL(2,16)$

# 439: 5-(18,8,104)

clan: 9-(20,10,4), 2 times reduced t, 2 times derived
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.
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.
$C_2\times PGL(2,8)$
\cite{Kramer75}

# 440: 5-(18,9,260)

clan: 9-(20,10,4), 2 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction with complementary design for 5-(17,8,80) (# 438)
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.
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.
\cite{Brouwer86} $Hol(C_17)+$
\cite{Brouwer86} Alltop(res(5-(18,8,104))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

# 441: 5-(17,9,180)

clan: 9-(20,10,4), 1 times reduced t, 1 times derived, 2 times residual
complementary design of 5-(17,8,80) (# 438)

# 442: 5-(19,9,364)

clan: 9-(20,10,4), 3 times reduced t, 1 times derived
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.
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.
$ {\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)
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.
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.
\cite{Krameretal85} $PSL(2,19)$

# 444: 5-(19,10,728)

clan: 9-(20,10,4), 3 times reduced t, 1 times residual
complementary design of 5-(19,9,364) (# 442)

# 445: 5-(16,7,25)

clan: 9-(20,10,5), 3 times derived, 1 times residual
$A_4\times A_4$
$C_4\times A_4$
$Hol(C_8)\times C_2$ 1259640 solutions

# 446: 5-(17,7,30)

clan: 9-(20,10,5), 1 times reduced t, 3 times derived
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
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
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.
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
Tran van Trung construction with complementary design for 5-(17,8,100) (# 447)
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.
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
\cite{Kramer75} $PGL(2,17)$ 3 isomorphism types

# 450: 5-(17,9,225)

clan: 9-(20,10,5), 1 times reduced t, 1 times derived, 2 times residual
complementary design of 5-(17,8,100) (# 447)

# 451: 5-(19,9,455)

clan: 9-(20,10,5), 3 times reduced t, 1 times derived
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.
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.
$ {\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)
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.
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.
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

# 453: 5-(19,10,910)

clan: 9-(20,10,5), 3 times reduced t, 1 times residual
complementary design of 5-(19,9,455) (# 451)

# 454: 5-(168,6,1)

clan: 161-(324,162,1), 156 times derived
$PSL(2,167)$ \cite{Mathon} >= 4 isomorphism types

# 455: 5-(17,7,12)

clan: 9-(20,10,2), 1 times reduced t, 3 times derived
Brouwer 1977/1986

# 456: 5-(17,7,36)

clan: 9-(20,10,6), 1 times reduced t, 3 times derived
$Hol(C_{17})$

# 457: 5-(18,6,4)

clan: 11-(24,12,4), 6 times derived
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
derived from 6-(19,7,4) (# 8609)

# 458: 5-(18,6,5)

clan: 11-(24,12,5), 6 times derived
\cite{Brouwer86}

# 459: 5-(18,7,12)

clan: 11-(24,12,2), 5 times derived, 1 times residual
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

# 460: 5-(18,7,18)

clan: 11-(24,12,3), 5 times derived, 1 times residual
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

# 461: 5-(18,7,24)

clan: 11-(24,12,4), 5 times derived, 1 times residual
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
residual design of 6-(19,7,4) (# 8609)

# 462: 5-(19,7,28)

clan: 11-(24,12,4), 1 times reduced t, 5 times derived
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)

clan: 11-(24,12,5), 5 times derived, 1 times residual
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

# 464: 5-(19,7,35)

clan: 11-(24,12,5), 1 times reduced t, 5 times derived
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)

clan: 11-(24,12,6), 5 times derived, 1 times residual
\cite{Kramer75} $PGL(2,17)$ 4 isomorphism types
residual design of 6-(19,7,6) (# 8613)

# 466: 5-(18,7,6)

clan: 11-(24,12,1), 5 times derived, 1 times residual
\cite{Kramer75} $PGL(2,17)$ 1 isomorphism type, block-transitive

# 467: 5-(18,8,102)

clan: 7-(20,10,102), 2 times derived
$C_2\times ASL(2,3)$

# 468: 5-(18,8,108)

clan: 7-(20,10,108), 2 times derived
\cite{Kramer75} $PGL(2,17)$ 12 isomorphism types

# 469: 5-(18,8,110)

clan: 11-(24,12,5), 4 times derived, 2 times residual
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types $PGL(2,16)+$ 32 isomorphism types

# 470: 5-(19,8,140)

clan: 11-(24,12,5), 1 times reduced t, 4 times derived, 1 times residual
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)