t designs with small t, id ge 600

---

# 600: 5-(18,9,180)

• clan: 7-(20,10,72), 1 times derived, 1 times residual
• $PSL(2,17)$ 5 isomorphism types
• \cite{Brouwer86} $Hol(C_17)+$
• \cite{Kramer75}

---

# 601: 5-(19,9,252)

• clan: 7-(20,10,72), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,180) (# 600) : der= 5-(18,8,72) and res= 5-(18,9,180) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 602: 5-(20,10,756)

• clan: 7-(20,10,72), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,252) (# 601)
• Tran van Trung construction (right) for 5-(19,9,252) (# 601) : der= 5-(19,9,252) and res= 5-(19,10,504) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,504) (# 603) : der= 5-(19,9,252) and res= 5-(19,10,504) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$

---

# 603: 5-(19,10,504)

• clan: 7-(20,10,72), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,252) (# 601)

---

# 604: 5-(18,9,185)

• clan: 7-(20,10,74), 1 times derived, 1 times residual
• $PSL(2,17)$ 1 isomorphism type
• \cite{Kramer75}

---

# 605: 5-(18,9,190)

• clan: 7-(20,10,76), 1 times derived, 1 times residual
• $PSL(2,8)\times C_2$ many isomorphism types
• \cite{Brouwer86} Alltop(res(5-(18,8,76))
• \cite{Kramer75}

---

# 606: 5-(19,9,266)

• clan: 7-(20,10,76), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,190) (# 605) : der= 5-(18,8,76) and res= 5-(18,9,190) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 607: 5-(20,10,798)

• clan: 7-(20,10,76), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,266) (# 606)
• Tran van Trung construction (right) for 5-(19,9,266) (# 606) : der= 5-(19,9,266) and res= 5-(19,10,532) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,532) (# 608) : der= 5-(19,9,266) and res= 5-(19,10,532) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$
• \cite{TranvanTrung86}

---

# 608: 5-(19,10,532)

• clan: 7-(20,10,76), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,266) (# 606)

---

# 609: 5-(18,9,200)

• clan: 7-(20,10,80), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,80))
• \cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

---

# 610: 5-(19,9,280)

• clan: 7-(20,10,80), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,200) (# 609) : der= 5-(18,8,80) and res= 5-(18,9,200) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 611: 5-(20,10,840)

• clan: 7-(20,10,80), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,280) (# 610)
• Tran van Trung construction (right) for 5-(19,9,280) (# 610) : der= 5-(19,9,280) and res= 5-(19,10,560) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,560) (# 612) : der= 5-(19,9,280) and res= 5-(19,10,560) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$

---

# 612: 5-(19,10,560)

• clan: 7-(20,10,80), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,280) (# 610)

---

# 613: 5-(18,9,205)

• clan: 7-(20,10,82), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,17)$ 1 isomorphism type
• \cite{Brouwer86} Alltop(res(5-(18,8,82))

---

# 614: 5-(19,9,287)

• clan: 7-(20,10,82), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,205) (# 613) : der= 5-(18,8,82) and res= 5-(18,9,205) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 615: 5-(20,10,861)

• clan: 7-(20,10,82), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,287) (# 614)
• Tran van Trung construction (right) for 5-(19,9,287) (# 614) : der= 5-(19,9,287) and res= 5-(19,10,574) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,574) (# 616) : der= 5-(19,9,287) and res= 5-(19,10,574) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$
• \cite{TranvanTrung86}

---

# 616: 5-(19,10,574)

• clan: 7-(20,10,82), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,287) (# 614)

---

# 617: 5-(18,9,210)

• clan: 7-(20,10,84), 1 times derived, 1 times residual
• $PSL(2,17)$ 1 isomorphism type
• $PSL(2,8)\times C_2$ many isomorphism types
• \cite{Brouwer86} $Hol(C_17)+$
• \cite{Kramer75}

---

# 618: 5-(19,9,294)

• clan: 7-(20,10,84), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,210) (# 617) : der= 5-(18,8,84) and res= 5-(18,9,210) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 619: 5-(20,10,882)

• clan: 7-(20,10,84), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,294) (# 618)
• Tran van Trung construction (right) for 5-(19,9,294) (# 618) : der= 5-(19,9,294) and res= 5-(19,10,588) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,588) (# 620) : der= 5-(19,9,294) and res= 5-(19,10,588) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$

---

# 620: 5-(19,10,588)

• clan: 7-(20,10,84), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,294) (# 618)

---

# 621: 5-(18,9,215)

• clan: 7-(20,10,86), 1 times derived, 1 times residual
• $PSL(2,17)$ 2 isomorphism types
• \cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

---

# 622: 5-(19,9,301)

• clan: 7-(20,10,86), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,215) (# 621) : der= 5-(18,8,86) and res= 5-(18,9,215) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 623: 5-(20,10,903)

• clan: 7-(20,10,86), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,301) (# 622)
• Tran van Trung construction (right) for 5-(19,9,301) (# 622) : der= 5-(19,9,301) and res= 5-(19,10,602) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,602) (# 624) : der= 5-(19,9,301) and res= 5-(19,10,602) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$

---

# 624: 5-(19,10,602)

• clan: 7-(20,10,86), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,301) (# 622)

---

# 625: 5-(18,9,220)

• clan: 11-(24,12,4), 3 times derived, 3 times residual
• $PSL(2,17)$ 9 isomorphism types
• \cite{Brouwer86} $Hol(C_17)+$
• \cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type

---

# 626: 5-(19,9,308)

• clan: 11-(24,12,4), 1 times reduced t, 3 times derived, 2 times residual
• Tran van Trung construction (left) for 5-(18,9,220) (# 625) : der= 5-(18,8,88) and res= 5-(18,9,220) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
• residual design of 6-(20,9,112) (# 8669)

---

# 627: 5-(20,10,924)

• clan: 11-(24,12,4), 2 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 5-(19,9,308) (# 626)
• Tran van Trung construction (right) for 5-(19,9,308) (# 626) : der= 5-(19,9,308) and res= 5-(19,10,616) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,616) (# 628) : der= 5-(19,9,308) and res= 5-(19,10,616) - the given design is the residual.
• \cite{Krameretal85}

---

# 628: 5-(19,10,616)

• clan: 11-(24,12,4), 1 times reduced t, 2 times derived, 3 times residual
• complementary design of 5-(19,9,308) (# 626)

---

# 629: 5-(20,9,420)

• clan: 11-(24,12,4), 2 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(19,9,308) (# 626) : der= 5-(19,8,112) and res= 5-(19,9,308) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$
• design 6-(20,9,112) (# 8669) with respect to smaller t
• residual design of 6-(21,9,140) (# 8670)

---

# 630: 5-(21,10,1344)

• clan: 11-(24,12,4), 3 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(20,10,924) (# 627) : der= 5-(20,9,420) and res= 5-(20,10,924) - the given design is the residual.
• Tran van Trung construction (right) for 5-(20,9,420) (# 629) : der= 5-(20,9,420) and res= 5-(20,10,924) - the given design is the derived.

---

# 631: 5-(21,9,560)

• clan: 11-(24,12,4), 3 times reduced t, 3 times derived
• Tran van Trung construction (left) for 5-(20,9,420) (# 629) : der= 5-(20,8,140) and res= 5-(20,9,420) - the given design is the residual.
• design 6-(21,9,140) (# 8670) with respect to smaller t

---

# 632: 5-(22,11,3808)

• clan: 11-(24,12,4), 4 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 5-(21,10,1344) (# 630)
• Tran van Trung construction (right) for 5-(21,10,1344) (# 630) : der= 5-(21,10,1344) and res= 5-(21,11,2464) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,11,2464) (# 633) : der= 5-(21,10,1344) and res= 5-(21,11,2464) - the given design is the residual.
• \cite{Kreher95}

---

# 633: 5-(21,11,2464)

• clan: 11-(24,12,4), 3 times reduced t, 1 times derived, 2 times residual
• complementary design of 5-(21,10,1344) (# 630)

---

# 634: 5-(22,10,1904)

• clan: 11-(24,12,4), 4 times reduced t, 2 times derived
• Tran van Trung construction (left) for 5-(21,10,1344) (# 630) : der= 5-(21,9,560) and res= 5-(21,10,1344) - the given design is the residual.
• Tran van Trung construction (right) for 5-(21,9,560) (# 631) : der= 5-(21,9,560) and res= 5-(21,10,1344) - the given design is the derived.
• \cite{Kreher95}

---

# 635: 5-(23,11,5712)

• clan: 11-(24,12,4), 5 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(22,11,3808) (# 632) : der= 5-(22,10,1904) and res= 5-(22,11,3808) - the given design is the residual.
• Tran van Trung construction (right) for 5-(22,10,1904) (# 634) : der= 5-(22,10,1904) and res= 5-(22,11,3808) - the given design is the derived.

---

# 636: 5-(24,12,15504)

• clan: 11-(24,12,4), 6 times reduced t
• Tran van Trung construction with complementary design for 5-(23,11,5712) (# 635)
• $ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23
• \cite{Bluskov}

---

# 637: 5-(18,9,225)

• clan: 7-(20,10,90), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

---

# 638: 5-(19,9,315)

• clan: 7-(20,10,90), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,225) (# 637) : der= 5-(18,8,90) and res= 5-(18,9,225) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 639: 5-(20,10,945)

• clan: 7-(20,10,90), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,315) (# 638)
• Tran van Trung construction (right) for 5-(19,9,315) (# 638) : der= 5-(19,9,315) and res= 5-(19,10,630) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,630) (# 640) : der= 5-(19,9,315) and res= 5-(19,10,630) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$

---

# 640: 5-(19,10,630)

• clan: 7-(20,10,90), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,315) (# 638)

---

# 641: 5-(18,9,230)

• clan: 7-(20,10,92), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,92))
• \cite{Kramer75}

---

# 642: 5-(19,9,322)

• clan: 7-(20,10,92), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,230) (# 641) : der= 5-(18,8,92) and res= 5-(18,9,230) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 643: 5-(20,10,966)

• clan: 7-(20,10,92), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,322) (# 642)
• Tran van Trung construction (right) for 5-(19,9,322) (# 642) : der= 5-(19,9,322) and res= 5-(19,10,644) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,644) (# 644) : der= 5-(19,9,322) and res= 5-(19,10,644) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$

---

# 644: 5-(19,10,644)

• clan: 7-(20,10,92), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,322) (# 642)

---

# 645: 5-(18,9,235)

• clan: 7-(20,10,94), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,94))
• \cite{Kramer75} $PGL(2,16)+$ 1 isomorphism type
• \cite{Kramer75} $PGL(2,17)$ 2 isomorphism types

---

# 646: 5-(19,9,329)

• clan: 7-(20,10,94), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,235) (# 645) : der= 5-(18,8,94) and res= 5-(18,9,235) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 647: 5-(20,10,987)

• clan: 7-(20,10,94), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,329) (# 646)
• Tran van Trung construction (right) for 5-(19,9,329) (# 646) : der= 5-(19,9,329) and res= 5-(19,10,658) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,658) (# 648) : der= 5-(19,9,329) and res= 5-(19,10,658) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$
• \cite{TranvanTrung86}

---

# 648: 5-(19,10,658)

• clan: 7-(20,10,94), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,329) (# 646)

---

# 649: 5-(18,9,240)

• clan: 7-(20,10,96), 1 times derived, 1 times residual
• $PSL(2,17)$ 1 isomorphism type
• \cite{Brouwer86} Alltop(res(5-(18,8,96))
• \cite{Kramer75} $PGL(2,16)+$ 4 isomorphism types

---

# 650: 5-(19,9,336)

• clan: 7-(20,10,96), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,240) (# 649) : der= 5-(18,8,96) and res= 5-(18,9,240) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+
• derived from 6-(20,10,336) (# 8655)

---

# 651: 5-(20,10,1008)

• clan: 7-(20,10,96), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,336) (# 650)
• Tran van Trung construction (right) for 5-(19,9,336) (# 650) : der= 5-(19,9,336) and res= 5-(19,10,672) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,672) (# 652) : der= 5-(19,9,336) and res= 5-(19,10,672) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$
• \cite{TranvanTrung86}
• design 6-(20,10,336) (# 8655) with respect to smaller t

---

# 652: 5-(19,10,672)

• clan: 7-(20,10,96), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,336) (# 650)
• residual design of 6-(20,10,336) (# 8655)

---

# 653: 5-(18,9,245)

• clan: 7-(20,10,98), 1 times derived, 1 times residual
• \cite{Brouwer86} Alltop(res(5-(18,8,98))
• \cite{Kramer75}

---

# 654: 5-(19,9,343)

• clan: 7-(20,10,98), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,245) (# 653) : der= 5-(18,8,98) and res= 5-(18,9,245) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 655: 5-(20,10,1029)

• clan: 7-(20,10,98), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,343) (# 654)
• Tran van Trung construction (right) for 5-(19,9,343) (# 654) : der= 5-(19,9,343) and res= 5-(19,10,686) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,686) (# 656) : der= 5-(19,9,343) and res= 5-(19,10,686) - the given design is the residual.
• \cite{Krameretal85}
• \cite{TranvanTrung86}

---

# 656: 5-(19,10,686)

• clan: 7-(20,10,98), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,343) (# 654)

---

# 657: 5-(18,9,250)

• clan: 7-(20,10,100), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
• \cite{Brouwer86} $Hol(C_17)+$

---

# 658: 5-(18,9,255)

• clan: 7-(20,10,102), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,16)+$ 4 isomorphism types
• \cite{Kramer75} $PGL(2,17)$ 3 isomorphism types

---

# 659: 5-(19,9,357)

• clan: 7-(20,10,102), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,255) (# 658) : der= 5-(18,8,102) and res= 5-(18,9,255) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 660: 5-(20,10,1071)

• clan: 7-(20,10,102), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,357) (# 659)
• Tran van Trung construction (right) for 5-(19,9,357) (# 659) : der= 5-(19,9,357) and res= 5-(19,10,714) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,714) (# 661) : der= 5-(19,9,357) and res= 5-(19,10,714) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$

---

# 661: 5-(19,10,714)

• clan: 7-(20,10,102), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,357) (# 659)

---

# 662: 5-(18,9,265)

• clan: 7-(20,10,106), 1 times derived, 1 times residual
• $Ico\times Octa$ 1280 solutions
• \cite{Kramer75} $PGL(2,17)$ 6 isomorphism types

---

# 663: 5-(18,9,270)

• clan: 7-(20,10,108), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,17)$ 3 isomorphism types
• \cite{Brouwer86} Alltop(res(5-(18,8,108))

---

# 664: 5-(19,9,378)

• clan: 7-(20,10,108), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,270) (# 663) : der= 5-(18,8,108) and res= 5-(18,9,270) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 665: 5-(20,10,1134)

• clan: 7-(20,10,108), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,378) (# 664)
• Tran van Trung construction (right) for 5-(19,9,378) (# 664) : der= 5-(19,9,378) and res= 5-(19,10,756) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,756) (# 666) : der= 5-(19,9,378) and res= 5-(19,10,756) - the given design is the residual.
• \cite{Krameretal85}
• \cite{TranvanTrung86}

---

# 666: 5-(19,10,756)

• clan: 7-(20,10,108), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,378) (# 664)

---

# 667: 5-(18,9,275)

• clan: 11-(24,12,5), 3 times derived, 3 times residual
• $PSL(2,17)$ 9 isomorphism types
• \cite{Brouwer86} Alltop(res(5-(18,8,110))
• \cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

---

# 668: 5-(19,9,385)

• clan: 11-(24,12,5), 1 times reduced t, 3 times derived, 2 times residual
• Tran van Trung construction (left) for 5-(18,9,275) (# 667) : der= 5-(18,8,110) and res= 5-(18,9,275) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 669: 5-(20,10,1155)

• clan: 11-(24,12,5), 2 times reduced t, 2 times derived, 2 times residual
• Tran van Trung construction with complementary design for 5-(19,9,385) (# 668)
• Tran van Trung construction (right) for 5-(19,9,385) (# 668) : der= 5-(19,9,385) and res= 5-(19,10,770) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,770) (# 670) : der= 5-(19,9,385) and res= 5-(19,10,770) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$
• \cite{TranvanTrung86}
• residual design of 6-(21,10,525) (# 8671)
• derived from 6-(21,11,1155) (# 8674)
• residual design of supplementary of 6-(21,10,840) (# 8680)
• derived from supplementary of 6-(21,11,1848) (# 8681)

---

# 670: 5-(19,10,770)

• clan: 11-(24,12,5), 1 times reduced t, 2 times derived, 3 times residual
• complementary design of 5-(19,9,385) (# 668)

---

# 671: 5-(20,9,525)

• clan: 11-(24,12,5), 2 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(19,9,385) (# 668) : der= 5-(19,8,140) and res= 5-(19,9,385) - the given design is the residual.
• TvT: 5-(19,8,140) $\cup$ 5-(19,9,385) \cite{TranvanTrung86}
• derived from 6-(21,10,525) (# 8671)
• derived from supplementary of 6-(21,10,840) (# 8680)

---

# 672: 5-(21,10,1680)

• clan: 11-(24,12,5), 3 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(20,10,1155) (# 669) : der= 5-(20,9,525) and res= 5-(20,10,1155) - the given design is the residual.
• Tran van Trung construction (right) for 5-(20,9,525) (# 671) : der= 5-(20,9,525) and res= 5-(20,10,1155) - the given design is the derived.
• design 6-(21,10,525) (# 8671) with respect to smaller t
• derived from 6-(22,11,1680) (# 8672)
• derived from supplementary of 6-(22,11,2688) (# 8679)
• supplementary design of 6-(21,10,840) (# 8680) with respect to smaller t

---

# 673: 5-(21,9,700)

• clan: 11-(24,12,5), 3 times reduced t, 3 times derived
• Tran van Trung construction (left) for 5-(20,9,525) (# 671) : der= 5-(20,8,175) and res= 5-(20,9,525) - the given design is the residual.

---

# 674: 5-(22,11,4760)

• clan: 11-(24,12,5), 4 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 5-(21,10,1680) (# 672)
• Tran van Trung construction (right) for 5-(21,10,1680) (# 672) : der= 5-(21,10,1680) and res= 5-(21,11,3080) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,11,3080) (# 675) : der= 5-(21,10,1680) and res= 5-(21,11,3080) - the given design is the residual.
• \cite{Kreher95}
• design 6-(22,11,1680) (# 8672) with respect to smaller t
• supplementary design of 6-(22,11,2688) (# 8679) with respect to smaller t

---

# 675: 5-(21,11,3080)

• clan: 11-(24,12,5), 3 times reduced t, 1 times derived, 2 times residual
• complementary design of 5-(21,10,1680) (# 672)
• residual design of 6-(22,11,1680) (# 8672)
• design 6-(21,11,1155) (# 8674) with respect to smaller t
• residual design of supplementary of 6-(22,11,2688) (# 8679)
• supplementary design of 6-(21,11,1848) (# 8681) with respect to smaller t
• Tran van Trung construction (left) for 5-(20,11,1925) (# 8682) : der= 5-(20,10,1155) and res= 5-(20,11,1925) - the given design is the residual.

---

# 676: 5-(22,10,2380)

• clan: 11-(24,12,5), 4 times reduced t, 2 times derived
• Tran van Trung construction (left) for 5-(21,10,1680) (# 672) : der= 5-(21,9,700) and res= 5-(21,10,1680) - the given design is the residual.
• Tran van Trung construction (right) for 5-(21,9,700) (# 673) : der= 5-(21,9,700) and res= 5-(21,10,1680) - the given design is the derived.
• $PSL(3,4)- \cup C2$
• \cite{Kreher95}

---

# 677: 5-(23,11,7140)

• clan: 11-(24,12,5), 5 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(22,11,4760) (# 674) : der= 5-(22,10,2380) and res= 5-(22,11,4760) - the given design is the residual.
• Tran van Trung construction (right) for 5-(22,10,2380) (# 676) : der= 5-(22,10,2380) and res= 5-(22,11,4760) - the given design is the derived.

---

# 678: 5-(24,12,19380)

• clan: 11-(24,12,5), 6 times reduced t
• Tran van Trung construction with complementary design for 5-(23,11,7140) (# 677)
• $ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23
• \cite{Bluskov}

---

# 679: 5-(18,9,280)

• clan: 7-(20,10,112), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,17)$ 2 isomorphism types
• \cite{Brouwer86} Alltop(res(5-(18,8,112))
• \cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types

---

# 680: 5-(19,9,392)

• clan: 7-(20,10,112), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,280) (# 679) : der= 5-(18,8,112) and res= 5-(18,9,280) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 681: 5-(20,10,1176)

• clan: 7-(20,10,112), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,392) (# 680)
• Tran van Trung construction (right) for 5-(19,9,392) (# 680) : der= 5-(19,9,392) and res= 5-(19,10,784) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,784) (# 682) : der= 5-(19,9,392) and res= 5-(19,10,784) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$
• \cite{TranvanTrung86}

---

# 682: 5-(19,10,784)

• clan: 7-(20,10,112), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,392) (# 680)

---

# 683: 5-(18,9,285)

• clan: 7-(20,10,114), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,17)$ 1 isomorphism type
• \cite{Brouwer86} Alltop(res(5-(18,8,114))

---

# 684: 5-(19,9,399)

• clan: 7-(20,10,114), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,285) (# 683) : der= 5-(18,8,114) and res= 5-(18,9,285) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 685: 5-(20,10,1197)

• clan: 7-(20,10,114), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,399) (# 684)
• Tran van Trung construction (right) for 5-(19,9,399) (# 684) : der= 5-(19,9,399) and res= 5-(19,10,798) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,798) (# 686) : der= 5-(19,9,399) and res= 5-(19,10,798) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$
• \cite{TranvanTrung86}

---

# 686: 5-(19,10,798)

• clan: 7-(20,10,114), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,399) (# 684)

---

# 687: 5-(18,9,295)

• clan: 7-(20,10,118), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,16)+$ 16 isomorphism types
• \cite{Kramer75} $PGL(2,17)$ 3 isomorphism types

---

# 688: 5-(19,9,413)

• clan: 7-(20,10,118), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,295) (# 687) : der= 5-(18,8,118) and res= 5-(18,9,295) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 689: 5-(20,10,1239)

• clan: 7-(20,10,118), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,413) (# 688)
• Tran van Trung construction (right) for 5-(19,9,413) (# 688) : der= 5-(19,9,413) and res= 5-(19,10,826) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,826) (# 690) : der= 5-(19,9,413) and res= 5-(19,10,826) - the given design is the residual.
• \cite{Krameretal85}

---

# 690: 5-(19,10,826)

• clan: 7-(20,10,118), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,413) (# 688)

---

# 691: 5-(18,9,30)

• clan: 7-(20,10,12), 1 times derived, 1 times residual
• \cite{Brouwer86} $Hol(C_17)+$ 1 isomorphism type
• \cite{Kramer75}

---

# 692: 5-(18,9,300)

• clan: 7-(20,10,120), 1 times derived, 1 times residual
• \cite{Kramer75} $PGL(2,17)$ 1 isomorphism type
• \cite{Brouwer86} $Hol(C_17)+$

---

# 693: 5-(19,9,420)

• clan: 7-(20,10,120), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,300) (# 692) : der= 5-(18,8,120) and res= 5-(18,9,300) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 694: 5-(20,10,1260)

• clan: 7-(20,10,120), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,420) (# 693)
• Tran van Trung construction (right) for 5-(19,9,420) (# 693) : der= 5-(19,9,420) and res= 5-(19,10,840) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,840) (# 695) : der= 5-(19,9,420) and res= 5-(19,10,840) - the given design is the residual.
• \cite{Krameretal85} $PGL(2,19)$

---

# 695: 5-(19,10,840)

• clan: 7-(20,10,120), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,420) (# 693)

---

# 696: 5-(18,9,305)

• clan: 7-(20,10,122), 1 times derived, 1 times residual
• $PSL(2,17)$ 6 isomorphism types
• \cite{Kramer75}

---

# 697: 5-(19,9,427)

• clan: 7-(20,10,122), 1 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(18,9,305) (# 696) : der= 5-(18,8,122) and res= 5-(18,9,305) - the given design is the residual.
• $ {\bf PSL(2,17)}^+ $ % -group 4 PSL 2 17 Add_fixpoint PSL_2_17+

---

# 698: 5-(20,10,1281)

• clan: 7-(20,10,122), 2 times reduced t
• Tran van Trung construction with complementary design for 5-(19,9,427) (# 697)
• Tran van Trung construction (right) for 5-(19,9,427) (# 697) : der= 5-(19,9,427) and res= 5-(19,10,854) - the given design is the derived.
• Tran van Trung construction (left) for 5-(19,10,854) (# 699) : der= 5-(19,9,427) and res= 5-(19,10,854) - the given design is the residual.
• \cite{Krameretal85} $PSL(2,19)$

---

# 699: 5-(19,10,854)

• clan: 7-(20,10,122), 1 times reduced t, 1 times residual
• complementary design of 5-(19,9,427) (# 697)

---

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created: Fri Oct 23 11:09:33 CEST 2009