t designs with small t, id ge 700

# 700: 5-(18,9,310)

clan: 7-(20,10,124), 1 times derived, 1 times residual
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,124))
residual design of 6-(19,9,124) (# 8631)
derived from 6-(19,10,310) (# 8634)
residual design of supplementary of 6-(19,9,162) (# 8638)
derived from supplementary of 6-(19,10,405) (# 8639)

# 701: 5-(19,9,434)

clan: 7-(20,10,124), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,310) (# 700) : der= 5-(18,8,124) and res= 5-(18,9,310) - the given design is the residual.
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
design 6-(19,9,124) (# 8631) with respect to smaller t
derived from 6-(20,10,434) (# 8632)
derived from supplementary of 6-(20,10,567) (# 8637)
supplementary design of 6-(19,9,162) (# 8638) with respect to smaller t

# 702: 5-(20,10,1302)

clan: 7-(20,10,124), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,434) (# 701)
Tran van Trung construction (right) for 5-(19,9,434) (# 701) : der= 5-(19,9,434) and res= 5-(19,10,868) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,868) (# 703) : der= 5-(19,9,434) and res= 5-(19,10,868) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}
design 6-(20,10,434) (# 8632) with respect to smaller t
supplementary design of 6-(20,10,567) (# 8637) with respect to smaller t

# 703: 5-(19,10,868)

clan: 7-(20,10,124), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,434) (# 701)
residual design of 6-(20,10,434) (# 8632)
design 6-(19,10,310) (# 8634) with respect to smaller t
residual design of supplementary of 6-(20,10,567) (# 8637)
supplementary design of 6-(19,10,405) (# 8639) with respect to smaller t
Tran van Trung construction (left) for 5-(18,10,558) (# 8640) : der= 5-(18,9,310) and res= 5-(18,10,558) - the given design is the residual.

# 704: 5-(18,9,315)

clan: 7-(20,10,126), 1 times derived, 1 times residual
$Ico\times Octa$ 35320 solutions
\cite{Kramer75} $PGL(2,17)$ 6 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,126))
residual design of 6-(19,9,126) (# 8643)
derived from 6-(19,10,315) (# 8646)
residual design of supplementary of 6-(19,9,160) (# 8650)
derived from supplementary of 6-(19,10,400) (# 8651)

# 705: 5-(19,9,441)

clan: 7-(20,10,126), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,315) (# 704) : der= 5-(18,8,126) and res= 5-(18,9,315) - the given design is the residual.
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
design 6-(19,9,126) (# 8643) with respect to smaller t
derived from 6-(20,10,441) (# 8644)
derived from supplementary of 6-(20,10,560) (# 8649)
supplementary design of 6-(19,9,160) (# 8650) with respect to smaller t

# 706: 5-(20,10,1323)

clan: 7-(20,10,126), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,441) (# 705)
Tran van Trung construction (right) for 5-(19,9,441) (# 705) : der= 5-(19,9,441) and res= 5-(19,10,882) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,882) (# 707) : der= 5-(19,9,441) and res= 5-(19,10,882) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}
design 6-(20,10,441) (# 8644) with respect to smaller t
supplementary design of 6-(20,10,560) (# 8649) with respect to smaller t

# 707: 5-(19,10,882)

clan: 7-(20,10,126), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,441) (# 705)
residual design of 6-(20,10,441) (# 8644)
design 6-(19,10,315) (# 8646) with respect to smaller t
residual design of supplementary of 6-(20,10,560) (# 8649)
supplementary design of 6-(19,10,400) (# 8651) with respect to smaller t
Tran van Trung construction (left) for 5-(18,10,567) (# 8652) : der= 5-(18,9,315) and res= 5-(18,10,567) - the given design is the residual.

# 708: 5-(18,9,320)

clan: 7-(20,10,128), 1 times derived, 1 times residual
$PSL(2,17)$ 9 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,128))
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

# 709: 5-(19,9,448)

clan: 7-(20,10,128), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,320) (# 708) : der= 5-(18,8,128) and res= 5-(18,9,320) - the given design is the residual.
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 710: 5-(20,10,1344)

clan: 7-(20,10,128), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,448) (# 709)
Tran van Trung construction (right) for 5-(19,9,448) (# 709) : der= 5-(19,9,448) and res= 5-(19,10,896) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,896) (# 711) : der= 5-(19,9,448) and res= 5-(19,10,896) - the given design is the residual.
\cite{TranvanTrung86}

# 711: 5-(19,10,896)

clan: 7-(20,10,128), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,448) (# 709)

# 712: 5-(18,9,330)

clan: 11-(24,12,6), 3 times derived, 3 times residual
\cite{Kramer75} $PGL(2,17)$ 4 isomorphism types
\cite{Brouwer86} $Hol(C_17)+$

# 713: 5-(19,9,462)

clan: 11-(24,12,6), 1 times reduced t, 3 times derived, 2 times residual
Tran van Trung construction (left) for 5-(18,9,330) (# 712) : der= 5-(18,8,132) and res= 5-(18,9,330) - the given design is the residual.
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 714: 5-(20,10,1386)

clan: 11-(24,12,6), 2 times reduced t, 2 times derived, 2 times residual
Tran van Trung construction with complementary design for 5-(19,9,462) (# 713)
Tran van Trung construction (right) for 5-(19,9,462) (# 713) : der= 5-(19,9,462) and res= 5-(19,10,924) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,924) (# 715) : der= 5-(19,9,462) and res= 5-(19,10,924) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$
residual design of 6-(21,10,630) (# 13138)
derived from 6-(21,11,1386) (# 13139)
residual design of supplementary of 6-(21,10,735) (# 13141)
derived from supplementary of 6-(21,11,1617) (# 13142)

# 715: 5-(19,10,924)

clan: 11-(24,12,6), 1 times reduced t, 2 times derived, 3 times residual
complementary design of 5-(19,9,462) (# 713)

# 716: 5-(20,9,630)

clan: 11-(24,12,6), 2 times reduced t, 3 times derived, 1 times residual
Tran van Trung construction (left) for 5-(19,9,462) (# 713) : der= 5-(19,8,168) and res= 5-(19,9,462) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$
derived from 6-(21,10,630) (# 13138)
derived from supplementary of 6-(21,10,735) (# 13141)

# 717: 5-(21,10,2016)

clan: 11-(24,12,6), 3 times reduced t, 2 times derived, 1 times residual
Tran van Trung construction (left) for 5-(20,10,1386) (# 714) : der= 5-(20,9,630) and res= 5-(20,10,1386) - the given design is the residual.
Tran van Trung construction (right) for 5-(20,9,630) (# 716) : der= 5-(20,9,630) and res= 5-(20,10,1386) - the given design is the derived.
$PGL(2,19)+$
residual design of 6-(22,10,840) (# 8696)
derived from 6-(22,11,2016) (# 8713)
design 6-(21,10,630) (# 13138) with respect to smaller t
derived from supplementary of 6-(22,11,2352) (# 13140)
supplementary design of 6-(21,10,735) (# 13141) with respect to smaller t

# 718: 5-(21,11,3696)

clan: 11-(24,12,6), 3 times reduced t, 1 times derived, 2 times residual
complementary design of 5-(21,10,2016) (# 717)
residual design of 6-(22,11,2016) (# 8713)
design 6-(21,11,1386) (# 13139) with respect to smaller t
residual design of supplementary of 6-(22,11,2352) (# 13140)
supplementary design of 6-(21,11,1617) (# 13142) with respect to smaller t
Tran van Trung construction (left) for 5-(20,11,2310) (# 13144) : der= 5-(20,10,1386) and res= 5-(20,11,2310) - the given design is the residual.

# 719: 5-(18,9,335)

clan: 7-(20,10,134), 1 times derived, 1 times residual
$PSL(2,17)$ 4 isomorphism types
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
residual design of 6-(19,9,134) (# 13116)
derived from 6-(19,10,335) (# 13117)
residual design of supplementary of 6-(19,9,152) (# 13119)
derived from supplementary of 6-(19,10,380) (# 13120)

# 720: 5-(18,9,340)

clan: 7-(20,10,136), 1 times derived, 1 times residual
$Ico\times Octa$ 19264 solutions
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
\cite{Kramer75} $PGL(2,16)+$ 4 isomorphism types

# 721: 5-(19,9,476)

clan: 7-(20,10,136), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,340) (# 720) : der= 5-(18,8,136) and res= 5-(18,9,340) - the given design is the residual.
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
derived from 6-(20,10,476) (# 8657)

# 722: 5-(20,10,1428)

clan: 7-(20,10,136), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,476) (# 721)
Tran van Trung construction (right) for 5-(19,9,476) (# 721) : der= 5-(19,9,476) and res= 5-(19,10,952) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,952) (# 723) : der= 5-(19,9,476) and res= 5-(19,10,952) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$
design 6-(20,10,476) (# 8657) with respect to smaller t

# 723: 5-(19,10,952)

clan: 7-(20,10,136), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,476) (# 721)
residual design of 6-(20,10,476) (# 8657)

# 724: 5-(18,9,345)

clan: 7-(20,10,138), 1 times derived, 1 times residual
\cite{Kramer75} $PGL(2,17)$ 4 isomorphism types

# 725: 5-(19,9,483)

clan: 7-(20,10,138), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,345) (# 724) : der= 5-(18,8,138) and res= 5-(18,9,345) - the given design is the residual.
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 726: 5-(20,10,1449)

clan: 7-(20,10,138), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,483) (# 725)
Tran van Trung construction (right) for 5-(19,9,483) (# 725) : der= 5-(19,9,483) and res= 5-(19,10,966) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,966) (# 727) : der= 5-(19,9,483) and res= 5-(19,10,966) - the given design is the residual.
\cite{Krameretal85}

# 727: 5-(19,10,966)

clan: 7-(20,10,138), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,483) (# 725)

# 728: 5-(18,9,35)

clan: 7-(20,10,14), 1 times derived, 1 times residual
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75}

# 729: 5-(19,9,49)

clan: 7-(20,10,14), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,35) (# 728) : der= 5-(18,8,14) and res= 5-(18,9,35) - the given design is the residual.

# 730: 5-(20,10,147)

clan: 7-(20,10,14), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,49) (# 729)
Tran van Trung construction (right) for 5-(19,9,49) (# 729) : der= 5-(19,9,49) and res= 5-(19,10,98) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,98) (# 731) : der= 5-(19,9,49) and res= 5-(19,10,98) - the given design is the residual.
\cite{Krameretal85} $PSL(2,19)$ 36 isomorphism types

# 731: 5-(19,10,98)

clan: 7-(20,10,14), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,49) (# 729)

# 732: 5-(18,9,350)

clan: 7-(20,10,140), 1 times derived, 1 times residual
$PSL(2,17)$ 2 isomorphism types
\cite{Brouwer86} Alltop(res(5-(18,8,140))
\cite{Kramer75}

# 733: 5-(19,9,490)

clan: 7-(20,10,140), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,350) (# 732) : der= 5-(18,8,140) and res= 5-(18,9,350) - the given design is the residual.
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 734: 5-(20,10,1470)

clan: 7-(20,10,140), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,490) (# 733)
Tran van Trung construction (right) for 5-(19,9,490) (# 733) : der= 5-(19,9,490) and res= 5-(19,10,980) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,980) (# 735) : der= 5-(19,9,490) and res= 5-(19,10,980) - the given design is the residual.
\cite{Krameretal85} $PSL(2,19)$
\cite{TranvanTrung86}

# 735: 5-(19,10,980)

clan: 7-(20,10,140), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,490) (# 733)

# 736: 5-(18,9,355)

clan: 7-(20,10,142), 1 times derived, 1 times residual
\cite{Brouwer86} Alltop(res(5-(18,8,142))
\cite{Kramer75} $PGL(2,16)+$ 4 isomorphism types
\cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

# 737: 5-(19,9,497)

clan: 7-(20,10,142), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,355) (# 736) : der= 5-(18,8,142) and res= 5-(18,9,355) - the given design is the residual.
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 738: 5-(20,10,1491)

clan: 7-(20,10,142), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,497) (# 737)
Tran van Trung construction (right) for 5-(19,9,497) (# 737) : der= 5-(19,9,497) and res= 5-(19,10,994) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,994) (# 739) : der= 5-(19,9,497) and res= 5-(19,10,994) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$
\cite{TranvanTrung86}

# 739: 5-(19,10,994)

clan: 7-(20,10,142), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,497) (# 737)

# 740: 5-(18,9,40)

clan: 7-(20,10,16), 1 times derived, 1 times residual
\cite{Brouwer86} Alltop(res(5-(18,8,16)) $Hol(C_17)+$
\cite{Kramer75}

# 741: 5-(19,9,56)

clan: 7-(20,10,16), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,40) (# 740) : der= 5-(18,8,16) and res= 5-(18,9,40) - the given design is the residual.

# 742: 5-(20,10,168)

clan: 7-(20,10,16), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,56) (# 741)
Tran van Trung construction (right) for 5-(19,9,56) (# 741) : der= 5-(19,9,56) and res= 5-(19,10,112) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,112) (# 743) : der= 5-(19,9,56) and res= 5-(19,10,112) - the given design is the residual.
\cite{Krameretal85} $PSL(2,19)$ 1 isomorphism type

# 743: 5-(19,10,112)

clan: 7-(20,10,16), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,56) (# 741)

# 744: 5-(18,9,45)

clan: 7-(20,10,18), 1 times derived, 1 times residual
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75}

# 745: 5-(18,9,50)

clan: 7-(20,10,20), 1 times derived, 1 times residual
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75}

# 746: 5-(18,9,55)

clan: 11-(24,12,1), 3 times derived, 3 times residual
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75}

# 747: 5-(18,9,60)

clan: 7-(20,10,24), 1 times derived, 1 times residual
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75}

# 748: 5-(18,9,65)

clan: 9-(20,10,1), 2 times reduced t, 1 times derived, 1 times residual
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75}

# 749: 5-(18,9,70)

clan: 7-(20,10,28), 1 times derived, 1 times residual
\cite{Kramer75}

# 750: 5-(18,9,75)

clan: 7-(20,10,30), 1 times derived, 1 times residual
\cite{Brouwer86} Alltop(res(5-(18,8,30))
\cite{Kramer75}

# 751: 5-(19,9,105)

clan: 7-(20,10,30), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,75) (# 750) : der= 5-(18,8,30) and res= 5-(18,9,75) - the given design is the residual.

# 752: 5-(20,10,315)

clan: 7-(20,10,30), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,105) (# 751)
Tran van Trung construction (right) for 5-(19,9,105) (# 751) : der= 5-(19,9,105) and res= 5-(19,10,210) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,210) (# 753) : der= 5-(19,9,105) and res= 5-(19,10,210) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$ 6 isomorphism types

# 753: 5-(19,10,210)

clan: 7-(20,10,30), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,105) (# 751)

# 754: 5-(18,9,80)

clan: 7-(20,10,32), 1 times derived, 1 times residual
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

# 755: 5-(19,9,112)

clan: 7-(20,10,32), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,80) (# 754) : der= 5-(18,8,32) and res= 5-(18,9,80) - the given design is the residual.

# 756: 5-(20,10,336)

clan: 7-(20,10,32), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,112) (# 755)
Tran van Trung construction (right) for 5-(19,9,112) (# 755) : der= 5-(19,9,112) and res= 5-(19,10,224) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,224) (# 757) : der= 5-(19,9,112) and res= 5-(19,10,224) - the given design is the residual.
$PSL(3,4)$
\cite{Krameretal85} $PSL(2,19)$ 89638 isomorphism types

# 757: 5-(19,10,224)

clan: 7-(20,10,32), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,112) (# 755)

# 758: 5-(18,9,85)

clan: 7-(20,10,34), 1 times derived, 1 times residual
\cite{Kramer75}

# 759: 5-(18,9,90)

clan: 7-(20,10,36), 1 times derived, 1 times residual
\cite{Brouwer86} $Hol(C_17)+$
\cite{Kramer75}

# 760: 5-(19,9,126)

clan: 7-(20,10,36), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,90) (# 759) : der= 5-(18,8,36) and res= 5-(18,9,90) - the given design is the residual.

# 761: 5-(20,10,378)

clan: 7-(20,10,36), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,126) (# 760)
Tran van Trung construction (right) for 5-(19,9,126) (# 760) : der= 5-(19,9,126) and res= 5-(19,10,252) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,252) (# 762) : der= 5-(19,9,126) and res= 5-(19,10,252) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$ 13 isomorphism types

# 762: 5-(19,10,252)

clan: 7-(20,10,36), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,126) (# 760)

# 763: 5-(18,9,95)

clan: 7-(20,10,38), 1 times derived, 1 times residual
\cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

# 764: 5-(19,9,133)

clan: 7-(20,10,38), 1 times reduced t, 1 times derived
Tran van Trung construction (left) for 5-(18,9,95) (# 763) : der= 5-(18,8,38) and res= 5-(18,9,95) - the given design is the residual.

# 765: 5-(20,10,399)

clan: 7-(20,10,38), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,133) (# 764)
Tran van Trung construction (right) for 5-(19,9,133) (# 764) : der= 5-(19,9,133) and res= 5-(19,10,266) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,266) (# 766) : der= 5-(19,9,133) and res= 5-(19,10,266) - the given design is the residual.
\cite{Krameretal85}

# 766: 5-(19,10,266)

clan: 7-(20,10,38), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,133) (# 764)

# 767: 5-(19,6,4)

clan: 5-(19,6,4)
$Hol(C_{19})$ (255 isom. types) \cite{Bettenetal98b}

# 768: 5-(19,6,6)

clan: 5-(19,6,6)
$Hol(C_{19})$ (17193 isom. types) no. of blocks = no. of 5-subsets \cite{Bettenetal98b}

# 769: 5-(19,7,42)

clan: 11-(24,12,6), 1 times reduced t, 5 times derived
Brouwer 1977/1986
design 6-(19,7,6) (# 8613) with respect to smaller t
Tran van Trung construction (right) for 5-(18,6,6) (# 8614) : der= 5-(18,6,6) and res= 5-(18,7,36) - the given design is the derived.

# 770: 5-(20,8,210)

clan: 11-(24,12,6), 2 times reduced t, 4 times derived
Tran van Trung construction (right) for 5-(19,7,42) (# 769) : der= 5-(19,7,42) and res= 5-(19,8,168) - the given design is the derived.
\cite{Krameretal85} $PGL(2,19)$ 644 isomorphism types

# 771: 5-(21,9,840)

clan: 11-(24,12,6), 3 times reduced t, 3 times derived
Tran van Trung construction (right) for 5-(20,8,210) (# 770) : der= 5-(20,8,210) and res= 5-(20,9,630) - the given design is the derived.
derived from 6-(22,10,840) (# 8696)

# 772: 5-(22,10,2856)

clan: 11-(24,12,6), 4 times reduced t, 2 times derived
Tran van Trung construction (right) for 5-(21,9,840) (# 771) : der= 5-(21,9,840) and res= 5-(21,10,2016) - the given design is the derived.
\cite{Kreher95}
design 6-(22,10,840) (# 8696) with respect to smaller t
derived from 6-(23,11,2856) (# 8714)
derived from supplementary of 6-(23,11,3332) (# 8721)

# 773: 5-(23,11,8568)

clan: 11-(24,12,6), 5 times reduced t, 1 times derived
Tran van Trung construction (right) for 5-(22,10,2856) (# 772) : der= 5-(22,10,2856) and res= 5-(22,11,5712) - the given design is the derived.
design 6-(23,11,2856) (# 8714) with respect to smaller t
derived from 6-(24,12,8568) (# 8715)
derived from supplementary of 6-(24,12,9996) (# 8720)
supplementary design of 6-(23,11,3332) (# 8721) with respect to smaller t

# 774: 5-(24,12,23256)

clan: 11-(24,12,6), 6 times reduced t
Tran van Trung construction with complementary design for 5-(23,11,8568) (# 773)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23
\cite{Bluskov}
design 6-(24,12,8568) (# 8715) with respect to smaller t
Tran van Trung construction (left) for 5-(23,12,14688) (# 8717) : der= 5-(23,11,8568) and res= 5-(23,12,14688) - the given design is the residual.
supplementary design of 6-(24,12,9996) (# 8720) with respect to smaller t

# 775: 5-(19,9,259)

clan: 7-(20,10,74), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 776: 5-(20,10,777)

clan: 7-(20,10,74), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,259) (# 775)
Tran van Trung construction (right) for 5-(19,9,259) (# 775) : der= 5-(19,9,259) and res= 5-(19,10,518) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,518) (# 777) : der= 5-(19,9,259) and res= 5-(19,10,518) - the given design is the residual.
\cite{Krameretal85} $PSL(2,19)$

# 777: 5-(19,10,518)

clan: 7-(20,10,74), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,259) (# 775)

# 778: 5-(19,9,350)

clan: 7-(20,10,100), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 779: 5-(20,10,1050)

clan: 7-(20,10,100), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,350) (# 778)
Tran van Trung construction (right) for 5-(19,9,350) (# 778) : der= 5-(19,9,350) and res= 5-(19,10,700) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,700) (# 780) : der= 5-(19,9,350) and res= 5-(19,10,700) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$

# 780: 5-(19,10,700)

clan: 7-(20,10,100), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,350) (# 778)

# 781: 5-(19,9,371)

clan: 7-(20,10,106), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 782: 5-(20,10,1113)

clan: 7-(20,10,106), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,371) (# 781)
Tran van Trung construction (right) for 5-(19,9,371) (# 781) : der= 5-(19,9,371) and res= 5-(19,10,742) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,742) (# 783) : der= 5-(19,9,371) and res= 5-(19,10,742) - the given design is the residual.
\cite{Krameretal85} $PGL(2,19)$

# 783: 5-(19,10,742)

clan: 7-(20,10,106), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,371) (# 781)

# 784: 5-(19,9,406)

clan: 7-(20,10,116), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
design 6-(19,9,116) (# 8618) with respect to smaller t
Tran van Trung construction (right) for 5-(18,8,116) (# 8619) : der= 5-(18,8,116) and res= 5-(18,9,290) - the given design is the derived.
derived from 6-(20,10,406) (# 8620)
derived from supplementary of 6-(20,10,595) (# 8625)
supplementary design of 6-(19,9,170) (# 8626) with respect to smaller t

# 785: 5-(20,10,1218)

clan: 7-(20,10,116), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,406) (# 784)
Tran van Trung construction (right) for 5-(19,9,406) (# 784) : der= 5-(19,9,406) and res= 5-(19,10,812) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,812) (# 786) : der= 5-(19,9,406) and res= 5-(19,10,812) - the given design is the residual.
\cite{Krameretal85} $PSL(2,19)$
design 6-(20,10,406) (# 8620) with respect to smaller t
supplementary design of 6-(20,10,595) (# 8625) with respect to smaller t

# 786: 5-(19,10,812)

clan: 7-(20,10,116), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,406) (# 784)
residual design of 6-(20,10,406) (# 8620)
design 6-(19,10,290) (# 8622) with respect to smaller t
residual design of supplementary of 6-(20,10,595) (# 8625)
supplementary design of 6-(19,10,425) (# 8627) with respect to smaller t
Tran van Trung construction (left) for 5-(18,10,522) (# 8628) : der= 5-(18,9,290) and res= 5-(18,10,522) - the given design is the residual.

# 787: 5-(19,9,469)

clan: 7-(20,10,134), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
derived from 6-(20,10,469) (# 8656)
design 6-(19,9,134) (# 13116) with respect to smaller t
derived from supplementary of 6-(20,10,532) (# 13118)
supplementary design of 6-(19,9,152) (# 13119) with respect to smaller t
Tran van Trung construction (right) for 5-(18,8,134) (# 13121) : der= 5-(18,8,134) and res= 5-(18,9,335) - the given design is the derived.

# 788: 5-(20,10,1407)

clan: 7-(20,10,134), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,469) (# 787)
Tran van Trung construction (right) for 5-(19,9,469) (# 787) : der= 5-(19,9,469) and res= 5-(19,10,938) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,938) (# 789) : der= 5-(19,9,469) and res= 5-(19,10,938) - the given design is the residual.
\cite{Krameretal85} $PSL(2,19)$
design 6-(20,10,469) (# 8656) with respect to smaller t
supplementary design of 6-(20,10,532) (# 13118) with respect to smaller t

# 789: 5-(19,10,938)

clan: 7-(20,10,134), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,469) (# 787)
residual design of 6-(20,10,469) (# 8656)
design 6-(19,10,335) (# 13117) with respect to smaller t
residual design of supplementary of 6-(20,10,532) (# 13118)
supplementary design of 6-(19,10,380) (# 13120) with respect to smaller t
Tran van Trung construction (left) for 5-(18,10,603) (# 13124) : der= 5-(18,9,335) and res= 5-(18,10,603) - the given design is the residual.

# 790: 5-(19,9,504)

clan: 7-(20,10,144), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 791: 5-(20,10,1512)

clan: 7-(20,10,144), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,504) (# 790)
Tran van Trung construction (right) for 5-(19,9,504) (# 790) : der= 5-(19,9,504) and res= 5-(19,10,1008) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,1008) (# 792) : der= 5-(19,9,504) and res= 5-(19,10,1008) - the given design is the residual.

# 792: 5-(19,10,1008)

clan: 7-(20,10,144), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,504) (# 790)

# 793: 5-(19,9,511)

clan: 7-(20,10,146), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 794: 5-(20,10,1533)

clan: 7-(20,10,146), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,511) (# 793)
Tran van Trung construction (right) for 5-(19,9,511) (# 793) : der= 5-(19,9,511) and res= 5-(19,10,1022) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,1022) (# 795) : der= 5-(19,9,511) and res= 5-(19,10,1022) - the given design is the residual.

# 795: 5-(19,10,1022)

clan: 7-(20,10,146), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,511) (# 793)

# 796: 5-(19,9,518)

clan: 7-(20,10,148), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 797: 5-(20,10,1554)

clan: 7-(20,10,148), 2 times reduced t
Tran van Trung construction with complementary design for 5-(19,9,518) (# 796)
Tran van Trung construction (right) for 5-(19,9,518) (# 796) : der= 5-(19,9,518) and res= 5-(19,10,1036) - the given design is the derived.
Tran van Trung construction (left) for 5-(19,10,1036) (# 798) : der= 5-(19,9,518) and res= 5-(19,10,1036) - the given design is the residual.

# 798: 5-(19,10,1036)

clan: 7-(20,10,148), 1 times reduced t, 1 times residual
complementary design of 5-(19,9,518) (# 796)

# 799: 5-(19,9,525)

clan: 7-(20,10,150), 1 times reduced t, 1 times derived
$ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
derived from supplementary of 6-(20,10,476) (# 8657)

created: Fri Oct 23 11:09:34 CEST 2009