t designs with small t, id ge 500

• clan: 7-(20,10,54), 2 times derived
• $Id_2\times PGL(2,8)$
• $C_2\times ASL(2,3)$ 1119 solutions
• $Id_2\times PGL(2,8)$

# 501: 5-(18,8,56)

• clan: 7-(20,10,56), 2 times derived
• $C_2\times ASL(2,3)$ 3012 solutions
• $C_2\times PGL(2,8)$ 1181 solutions

# 502: 5-(18,8,58)

• clan: 7-(20,10,58), 2 times derived
• $ASL(2,3)\times Id_2$ (many solutions)

# 503: 5-(18,8,6)

• clan: 7-(20,10,6), 2 times derived
• $PGL(2,16)+$ 1 isomorphism type
• \cite{MacWilliams78}

# 504: 5-(18,8,60)

• clan: 7-(20,10,60), 2 times derived
• \cite{Kramer75} $PGL(2,17)$ 4 isomorphism types

# 505: 5-(18,8,62)

• clan: 7-(20,10,62), 2 times derived
• $C_2\times ASL(2,3)$ 18287 solutions
• $C_2\times PGL(2,8)$ 1419 solutions
• \cite{Kramer75} $PGL(2,17)$ 5 isomorphism types

# 506: 5-(18,8,64)

• clan: 7-(20,10,64), 2 times derived
• $C_2\times ASL(2,3)$ 80502 solutions
• \cite{Kramer75} $PGL(2,17)$ 8 isomorphism types

# 507: 5-(18,8,66)

• clan: 11-(24,12,3), 4 times derived, 2 times residual
• $PSL(2,8)\times Id_2$ (many solutions)
• \cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

# 508: 5-(19,8,84)

• clan: 11-(24,12,3), 1 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(18,8,66) (# 507) : der= 5-(18,7,18) and res= 5-(18,8,66) - the given design is the residual.

# 509: 5-(18,8,68)

• clan: 7-(20,10,68), 2 times derived
• $ASL(2,3)\times Id_2$ (many solutions)

# 510: 5-(18,8,70)

• clan: 7-(20,10,70), 2 times derived
• $C_2\times PGL(2,8)$ 12426 solutions

# 511: 5-(18,8,72)

• clan: 7-(20,10,72), 2 times derived
• $C_2\times ASL(2,3)$

# 512: 5-(18,8,76)

• clan: 7-(20,10,76), 2 times derived
• $PSL(2,8)\times Id_2$ (many solutions)
• \cite{Kramer75} $PGL(2,17)$ 6 isomorphism types

# 513: 5-(18,8,80)

• clan: 7-(20,10,80), 2 times derived
• $C_2\times PGL(2,8)$
• \cite{Kramer75} $PGL(2,17)$ 9 isomorphism types

# 514: 5-(18,8,82)

• clan: 7-(20,10,82), 2 times derived
• \cite{Kramer75} $PGL(2,17)$ 4 isomorphism types

# 515: 5-(18,8,84)

• clan: 7-(20,10,84), 2 times derived
• $Id_2\times PGL(2,8)$

# 516: 5-(18,8,86)

• clan: 7-(20,10,86), 2 times derived
• $C_2\times ASL(2,3)$

# 517: 5-(18,8,88)

• clan: 11-(24,12,4), 4 times derived, 2 times residual
• $C_2\times ASL(2,3)$

# 518: 5-(19,8,112)

• clan: 11-(24,12,4), 1 times reduced t, 4 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(18,8,88) (# 517) : der= 5-(18,7,24) and res= 5-(18,8,88) - the given design is the residual.
• residual design of 6-(20,8,28) (# 8658)
• derived from 6-(20,9,112) (# 8669)

# 519: 5-(20,8,140)

• clan: 11-(24,12,4), 2 times reduced t, 4 times derived
• Tran van Trung construction (left) for 5-(19,8,112) (# 518) : der= 5-(19,7,28) and res= 5-(19,8,112) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 365 isomorphism types
• design 6-(20,8,28) (# 8658) with respect to smaller t
• derived from 6-(21,9,140) (# 8670)

# 520: 5-(18,8,90)

• clan: 7-(20,10,90), 2 times derived
• $Id_2\times PGL(2,8)$

# 521: 5-(18,8,92)

• clan: 7-(20,10,92), 2 times derived
• \cite{Kramer75} $PGL(2,17)$ 8 isomorphism types

# 522: 5-(18,8,94)

• clan: 7-(20,10,94), 2 times derived
• \cite{Kramer75} $PGL(2,17)$ 9 isomorphism types
• $C_2\times PGL(2,8)$

# 523: 5-(18,8,96)

• clan: 7-(20,10,96), 2 times derived
• \cite{Kramer75} $PGL(2,17)$ 6 isomorphism types

# 524: 5-(18,8,98)

• clan: 7-(20,10,98), 2 times derived
• \cite{Kramer75} $PGL(2,17)$ 6 isomorphism types

# 525: 5-(18,9,100)

• clan: 7-(20,10,40), 1 times derived, 1 times residual
• \cite{Brouwer86} $Hol(C_17)+$
• \cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type

# 526: 5-(19,9,140)

• clan: 7-(20,10,40), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,100) (# 525) : der= 5-(18,8,40) and res= 5-(18,9,100) - the given design is the residual.
• Brouwer 1977/1986

# 527: 5-(20,10,420)

• clan: 7-(20,10,40), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,140) (# 526)
• Tran van Trung construction (right) for 5-(19,9,140) (# 526) : der= 5-(19,9,140) and res= 5-(19,10,280) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,280) (# 528) : der= 5-(19,9,140) and res= 5-(19,10,280) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 104 isomorphism types

# 528: 5-(19,10,280)

• clan: 7-(20,10,40), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,140) (# 526)

# 529: 5-(18,9,105)

• clan: 7-(20,10,42), 1 times derived, 1 times residual
• $PSL(2,8)\times C_2$ 48 solutions

# 530: 5-(19,9,147)

• clan: 7-(20,10,42), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,105) (# 529) : der= 5-(18,8,42) and res= 5-(18,9,105) - the given design is the residual.

# 531: 5-(20,10,441)

• clan: 7-(20,10,42), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,147) (# 530)
• Tran van Trung construction (right) for 5-(19,9,147) (# 530) : der= 5-(19,9,147) and res= 5-(19,10,294) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,294) (# 532) : der= 5-(19,9,147) and res= 5-(19,10,294) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 72 isomorphism types

# 532: 5-(19,10,294)

• clan: 7-(20,10,42), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,147) (# 530)

# 533: 5-(18,9,110)

• clan: 11-(24,12,2), 3 times derived, 3 times residual
• \cite{Kramer75}

# 534: 5-(19,9,154)

• clan: 11-(24,12,2), 1 times reduced t, 3 times derived, 2 times residual
• Tran van Trung construction (left) for 5-(18,9,110) (# 533) : der= 5-(18,8,44) and res= 5-(18,9,110) - the given design is the residual.

# 535: 5-(20,10,462)

• clan: 11-(24,12,2), 2 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 5-(19,9,154) (# 534)
• Tran van Trung construction (right) for 5-(19,9,154) (# 534) : der= 5-(19,9,154) and res= 5-(19,10,308) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,308) (# 536) : der= 5-(19,9,154) and res= 5-(19,10,308) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$
• \cite{TranvanTrung86}

# 536: 5-(19,10,308)

• clan: 11-(24,12,2), 1 times reduced t, 2 times derived, 3 times residual
• complementary design of 5-(19,9,154) (# 534)

# 537: 5-(20,9,210)

• clan: 11-(24,12,2), 2 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(19,9,154) (# 534) : der= 5-(19,8,56) and res= 5-(19,9,154) - the given design is the residual.

# 538: 5-(21,10,672)

• clan: 11-(24,12,2), 3 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(20,10,462) (# 535) : der= 5-(20,9,210) and res= 5-(20,10,462) - the given design is the residual.
• Tran van Trung construction (right) for 5-(20,9,210) (# 537) : der= 5-(20,9,210) and res= 5-(20,10,462) - the given design is the derived.

# 539: 5-(22,11,1904)

• clan: 11-(24,12,2), 4 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 5-(21,10,672) (# 538)
• Tran van Trung construction (right) for 5-(21,10,672) (# 538) : der= 5-(21,10,672) and res= 5-(21,11,1232) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,11,1232) (# 540) : der= 5-(21,10,672) and res= 5-(21,11,1232) - the given design is the residual.
• \cite{Kreher95}

# 540: 5-(21,11,1232)

• clan: 11-(24,12,2), 3 times reduced t, 1 times derived, 2 times residual
• complementary design of 5-(21,10,672) (# 538)

# 541: 5-(18,9,115)

• clan: 7-(20,10,46), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,46))
• \cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type

# 542: 5-(19,9,161)

• clan: 7-(20,10,46), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,115) (# 541) : der= 5-(18,8,46) and res= 5-(18,9,115) - the given design is the residual.

# 543: 5-(20,10,483)

• clan: 7-(20,10,46), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,161) (# 542)
• Tran van Trung construction (right) for 5-(19,9,161) (# 542) : der= 5-(19,9,161) and res= 5-(19,10,322) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,322) (# 544) : der= 5-(19,9,161) and res= 5-(19,10,322) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 173 isomorphism types

# 544: 5-(19,10,322)

• clan: 7-(20,10,46), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,161) (# 542)

# 545: 5-(18,9,120)

• clan: 7-(20,10,48), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,48))
• \cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type
• \cite{Kramer75} $PGL(2,17)$ 1 isomorphism type

# 546: 5-(19,9,168)

• clan: 7-(20,10,48), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,120) (# 545) : der= 5-(18,8,48) and res= 5-(18,9,120) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 547: 5-(20,10,504)

• clan: 7-(20,10,48), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,168) (# 546)
• Tran van Trung construction (right) for 5-(19,9,168) (# 546) : der= 5-(19,9,168) and res= 5-(19,10,336) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,336) (# 548) : der= 5-(19,9,168) and res= 5-(19,10,336) - the given design is the residual.
• \cite{Krameretal85}
• \cite{TranvanTrung86}

# 548: 5-(19,10,336)

• clan: 7-(20,10,48), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,168) (# 546)

# 549: 5-(18,9,125)

• clan: 7-(20,10,50), 1 times derived, 1 times residual
• \cite{Kramer75}

# 550: 5-(19,9,175)

• clan: 7-(20,10,50), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,125) (# 549) : der= 5-(18,8,50) and res= 5-(18,9,125) - the given design is the residual.

# 551: 5-(20,10,525)

• clan: 7-(20,10,50), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,175) (# 550)
• Tran van Trung construction (right) for 5-(19,9,175) (# 550) : der= 5-(19,9,175) and res= 5-(19,10,350) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,350) (# 552) : der= 5-(19,9,175) and res= 5-(19,10,350) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$

# 552: 5-(19,10,350)

• clan: 7-(20,10,50), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,175) (# 550)

# 553: 5-(18,9,130)

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

# 554: 5-(19,9,182)

• clan: 9-(20,10,2), 3 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,130) (# 553) : der= 5-(18,8,52) and res= 5-(18,9,130) - the given design is the residual.

# 555: 5-(20,10,546)

• clan: 9-(20,10,2), 4 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,182) (# 554)
• Tran van Trung construction (right) for 5-(19,9,182) (# 554) : der= 5-(19,9,182) and res= 5-(19,10,364) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,364) (# 556) : der= 5-(19,9,182) and res= 5-(19,10,364) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 307 isomorphism types

# 556: 5-(19,10,364)

• clan: 9-(20,10,2), 3 times reduced t, 1 times residual
• complementary design of 5-(19,9,182) (# 554)

# 557: 5-(18,9,135)

• clan: 7-(20,10,54), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type
• \cite{Kramer75} $PSL(2,17)$ 2 isomorphism types

# 558: 5-(19,9,189)

• clan: 7-(20,10,54), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,135) (# 557) : der= 5-(18,8,54) and res= 5-(18,9,135) - the given design is the residual.

# 559: 5-(20,10,567)

• clan: 7-(20,10,54), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,189) (# 558)
• Tran van Trung construction (right) for 5-(19,9,189) (# 558) : der= 5-(19,9,189) and res= 5-(19,10,378) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,378) (# 560) : der= 5-(19,9,189) and res= 5-(19,10,378) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 567 isomorphism types

# 560: 5-(19,10,378)

• clan: 7-(20,10,54), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,189) (# 558)

# 561: 5-(18,9,140)

• clan: 7-(20,10,56), 1 times derived, 1 times residual
• \cite{Brouwer86} $Hol(C_17)+$
• \cite{Kramer75} $PSL(2,17)$ 1 isomorphism type

# 562: 5-(19,9,196)

• clan: 7-(20,10,56), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,140) (# 561) : der= 5-(18,8,56) and res= 5-(18,9,140) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 563: 5-(20,10,588)

• clan: 7-(20,10,56), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,196) (# 562)
• Tran van Trung construction (right) for 5-(19,9,196) (# 562) : der= 5-(19,9,196) and res= 5-(19,10,392) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,392) (# 564) : der= 5-(19,9,196) and res= 5-(19,10,392) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$

# 564: 5-(19,10,392)

• clan: 7-(20,10,56), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,196) (# 562)

# 565: 5-(18,9,145)

• clan: 7-(20,10,58), 1 times derived, 1 times residual
• \cite{Kramer75}

# 566: 5-(19,9,203)

• clan: 7-(20,10,58), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,145) (# 565) : der= 5-(18,8,58) and res= 5-(18,9,145) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 567: 5-(20,10,609)

• clan: 7-(20,10,58), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,203) (# 566)
• Tran van Trung construction (right) for 5-(19,9,203) (# 566) : der= 5-(19,9,203) and res= 5-(19,10,406) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,406) (# 568) : der= 5-(19,9,203) and res= 5-(19,10,406) - the given design is the residual.
• \cite{Krameretal85}

# 568: 5-(19,10,406)

• clan: 7-(20,10,58), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,203) (# 566)

# 569: 5-(18,9,15)

• clan: 7-(20,10,6), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,6))
• \cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type

# 570: 5-(19,9,21)

• clan: 7-(20,10,6), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,15) (# 569) : der= 5-(18,8,6) and res= 5-(18,9,15) - the given design is the residual.
• Brouwer 1977/1986

# 571: 5-(20,10,63)

• clan: 7-(20,10,6), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,21) (# 570)
• Tran van Trung construction (right) for 5-(19,9,21) (# 570) : der= 5-(19,9,21) and res= 5-(19,10,42) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,42) (# 572) : der= 5-(19,9,21) and res= 5-(19,10,42) - the given design is the residual.
• \cite{Krameretal85}

# 572: 5-(19,10,42)

• clan: 7-(20,10,6), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,21) (# 570)

# 573: 5-(18,9,150)

• clan: 7-(20,10,60), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,60))
• \cite{Kramer75}

# 574: 5-(19,9,210)

• clan: 7-(20,10,60), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,150) (# 573) : der= 5-(18,8,60) and res= 5-(18,9,150) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 575: 5-(20,10,630)

• clan: 7-(20,10,60), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,210) (# 574)
• Tran van Trung construction (right) for 5-(19,9,210) (# 574) : der= 5-(19,9,210) and res= 5-(19,10,420) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,420) (# 576) : der= 5-(19,9,210) and res= 5-(19,10,420) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 2106 isomorphism types

# 576: 5-(19,10,420)

• clan: 7-(20,10,60), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,210) (# 574)

# 577: 5-(18,9,155)

• clan: 7-(20,10,62), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,62))
• \cite{Kramer75} $PSL(2,17)$ 1 isomorphism type

# 578: 5-(19,9,217)

• clan: 7-(20,10,62), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,155) (# 577) : der= 5-(18,8,62) and res= 5-(18,9,155) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 579: 5-(20,10,651)

• clan: 7-(20,10,62), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,217) (# 578)
• Tran van Trung construction (right) for 5-(19,9,217) (# 578) : der= 5-(19,9,217) and res= 5-(19,10,434) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,434) (# 580) : der= 5-(19,9,217) and res= 5-(19,10,434) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$
• \cite{TranvanTrung86}

# 580: 5-(19,10,434)

• clan: 7-(20,10,62), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,217) (# 578)

# 581: 5-(18,9,160)

• clan: 7-(20,10,64), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,64))
• \cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
• \cite{Kramer75} $PSL(2,17)$ 1 isomorphism type

# 582: 5-(19,9,224)

• clan: 7-(20,10,64), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,160) (# 581) : der= 5-(18,8,64) and res= 5-(18,9,160) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 583: 5-(20,10,672)

• clan: 7-(20,10,64), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,224) (# 582)
• Tran van Trung construction (right) for 5-(19,9,224) (# 582) : der= 5-(19,9,224) and res= 5-(19,10,448) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,448) (# 584) : der= 5-(19,9,224) and res= 5-(19,10,448) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 3994 isomorphism types
• \cite{TranvanTrung86}

# 584: 5-(19,10,448)

• clan: 7-(20,10,64), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,224) (# 582)

# 585: 5-(18,9,165)

• clan: 11-(24,12,3), 3 times derived, 3 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,66))
• \cite{Kramer75}

# 586: 5-(19,9,231)

• clan: 11-(24,12,3), 1 times reduced t, 3 times derived, 2 times residual
• Tran van Trung construction (left) for 5-(18,9,165) (# 585) : der= 5-(18,8,66) and res= 5-(18,9,165) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 587: 5-(20,10,693)

• clan: 11-(24,12,3), 2 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 5-(19,9,231) (# 586)
• Tran van Trung construction (right) for 5-(19,9,231) (# 586) : der= 5-(19,9,231) and res= 5-(19,10,462) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,462) (# 588) : der= 5-(19,9,231) and res= 5-(19,10,462) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 3968 isomorphism types
• residual design of 6-(21,10,315) (# 13128)
• derived from 6-(21,11,693) (# 13129)
• residual design of supplementary of 6-(21,10,1050) (# 13131)
• derived from supplementary of 6-(21,11,2310) (# 13132)

# 588: 5-(19,10,462)

• clan: 11-(24,12,3), 1 times reduced t, 2 times derived, 3 times residual
• complementary design of 5-(19,9,231) (# 586)

# 589: 5-(20,9,315)

• clan: 11-(24,12,3), 2 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(19,9,231) (# 586) : der= 5-(19,8,84) and res= 5-(19,9,231) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$ 555 isomorphism types
• derived from 6-(21,10,315) (# 13128)
• derived from supplementary of 6-(21,10,1050) (# 13131)

# 590: 5-(21,10,1008)

• clan: 11-(24,12,3), 3 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(20,10,693) (# 587) : der= 5-(20,9,315) and res= 5-(20,10,693) - the given design is the residual.
• Tran van Trung construction (right) for 5-(20,9,315) (# 589) : der= 5-(20,9,315) and res= 5-(20,10,693) - the given design is the derived.
• $PGL(2,19)+$
• derived from 6-(22,11,1008) (# 8701)
• design 6-(21,10,315) (# 13128) with respect to smaller t
• derived from supplementary of 6-(22,11,3360) (# 13130)
• supplementary design of 6-(21,10,1050) (# 13131) with respect to smaller t

# 591: 5-(21,11,1848)

• clan: 11-(24,12,3), 3 times reduced t, 1 times derived, 2 times residual
• complementary design of 5-(21,10,1008) (# 590)
• residual design of 6-(22,11,1008) (# 8701)
• design 6-(21,11,693) (# 13129) with respect to smaller t
• residual design of supplementary of 6-(22,11,3360) (# 13130)
• supplementary design of 6-(21,11,2310) (# 13132) with respect to smaller t
• Tran van Trung construction (left) for 5-(20,11,1155) (# 13134) : der= 5-(20,10,693) and res= 5-(20,11,1155) - the given design is the residual.

# 592: 5-(18,9,170)

• clan: 7-(20,10,68), 1 times derived, 1 times residual
• \cite{Brouwer86} $Hol(C_17)+$

# 593: 5-(19,9,238)

• clan: 7-(20,10,68), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,170) (# 592) : der= 5-(18,8,68) and res= 5-(18,9,170) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 594: 5-(20,10,714)

• clan: 7-(20,10,68), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,238) (# 593)
• Tran van Trung construction (right) for 5-(19,9,238) (# 593) : der= 5-(19,9,238) and res= 5-(19,10,476) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,476) (# 595) : der= 5-(19,9,238) and res= 5-(19,10,476) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$

# 595: 5-(19,10,476)

• clan: 7-(20,10,68), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,238) (# 593)

# 596: 5-(18,9,175)

• clan: 7-(20,10,70), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
• \cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

# 597: 5-(19,9,245)

• clan: 7-(20,10,70), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,175) (# 596) : der= 5-(18,8,70) and res= 5-(18,9,175) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

# 598: 5-(20,10,735)

• clan: 7-(20,10,70), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,245) (# 597)
• Tran van Trung construction (right) for 5-(19,9,245) (# 597) : der= 5-(19,9,245) and res= 5-(19,10,490) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,490) (# 599) : der= 5-(19,9,245) and res= 5-(19,10,490) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$

# 599: 5-(19,10,490)

• clan: 7-(20,10,70), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,245) (# 597)

created: Fri Oct 23 11:09:32 CEST 2009