t designs with small t, id ge 8600

---

# 8600: 5-(64,8,5601)

• clan: 15-(74,18,5601), 10 times derived
• $AGL(3,4)$ many solutions

---

# 8601: 5-(64,8,6161)

• clan: 15-(74,18,6161), 10 times derived
• $AGL(3,4)$ many solutions

---

# 8602: 5-(64,8,8289)

• clan: 15-(74,18,8289), 10 times derived
• $AGL(3,4)$ many solutions

---

# 8603: 5-(64,8,10900)

• clan: 15-(74,18,10900), 10 times derived
• $AGL(3,4)$ many solutions

---

# 8604: 5-(64,8,11236)

• clan: 15-(74,18,11236), 10 times derived
• $AGL(3,4)$ many solutions

---

# 8605: 5-(66,6,20)

• clan: 59-(120,60,20), 54 times derived
• $P/Gamma L(2,32)\times C_2$ many solutions

---

# 8606: 5-(66,6,21)

• clan: 59-(120,60,21), 54 times derived
• $P/Gamma L(2,32)\times C_2$ many solutions

---

# 8607: 5-(72,6,1)

• clan: 65-(132,66,1), 60 times derived
• \cite{Mills78}\cite{Grannelletal98} $PSL(2,71)$ short orbits: 4204 isomorphism types, 916299 isomorphism types \cite{BettenMolodtsovLaueWassermann98}

---

# 8608: 5-(84,6,1)

• clan: 77-(156,78,1), 72 times derived
• \cite{Denniston76} $PSL(2,83)$ 38717 isomorphism types from short orbits \cite{Grannelletal98}, semiregular: 3 isomorphism types \cite{BettenMolodtsovLaueWassermann98}

---

# 8609: 6-(19,7,4)

• clan: 11-(24,12,4), 5 times derived
• $Hol(C_{17})++$ (1 isom. type) \cite{Bettenetal97b}

---

# 8610: 5-(19,7,63)

• clan: 11-(24,12,9), 1 times reduced t, 5 times derived
• supplementary design of 6-(19,7,4) (# 8609) with respect to smaller t
• Tran van Trung construction (right) for 5-(18,6,9) (# 8611) : der= 5-(18,6,9) and res= 5-(18,7,54) - the given design is the derived.
• Tran van Trung construction (left) for 5-(18,7,54) (# 8612) : der= 5-(18,6,9) and res= 5-(18,7,54) - the given design is the residual.
• derived from supplementary of 6-(20,8,28) (# 8658)

---

# 8611: 5-(18,6,9)

• clan: 11-(24,12,9), 6 times derived
• derived from supplementary of 6-(19,7,4) (# 8609)

---

# 8612: 5-(18,7,54)

• clan: 11-(24,12,9), 5 times derived, 1 times residual
• residual design of supplementary of 6-(19,7,4) (# 8609)

---

# 8613: 6-(19,7,6)

• clan: 11-(24,12,6), 5 times derived
• $Hol(C_{19})$ (3 isom. types) \cite{Bettenetal97b}

---

# 8614: 5-(18,6,6)

• clan: 11-(24,12,6), 6 times derived
• derived from 6-(19,7,6) (# 8613)

---

# 8615: 5-(19,7,49)

• clan: 11-(24,12,7), 1 times reduced t, 5 times derived
• supplementary design of 6-(19,7,6) (# 8613) with respect to smaller t
• Tran van Trung construction (right) for 5-(18,6,7) (# 8616) : der= 5-(18,6,7) and res= 5-(18,7,42) - the given design is the derived.
• Tran van Trung construction (left) for 5-(18,7,42) (# 8617) : der= 5-(18,6,7) and res= 5-(18,7,42) - the given design is the residual.

---

# 8616: 5-(18,6,7)

• clan: 11-(24,12,7), 6 times derived
• derived from supplementary of 6-(19,7,6) (# 8613)

---

# 8617: 5-(18,7,42)

• clan: 11-(24,12,7), 5 times derived, 1 times residual
• residual design of supplementary of 6-(19,7,6) (# 8613)

---

# 8618: 6-(19,9,116)

• clan: 7-(20,10,116), 1 times derived
• $(ASL(2,9)\times Id_2)+$ ($\ge 4000$ solutions)
• derived from 7-(20,10,116) (# 8621)
• derived from supplementary of 7-(20,10,170) (# 8630)

---

# 8619: 5-(18,8,116)

• clan: 7-(20,10,116), 2 times derived
• derived from 6-(19,9,116) (# 8618)
• derived from supplementary of 6-(19,9,170) (# 8626)

---

# 8620: 6-(20,10,406)

• clan: 7-(20,10,116), 1 times reduced t
• Tran van Trung construction with complementary design for 6-(19,9,116) (# 8618)
• Tran van Trung construction (right) for 6-(19,9,116) (# 8618) : der= 6-(19,9,116) and res= 6-(19,10,290) - the given design is the derived.
• design 7-(20,10,116) (# 8621) with respect to smaller t
• Tran van Trung construction (left) for 6-(19,10,290) (# 8622) : der= 6-(19,9,116) and res= 6-(19,10,290) - the given design is the residual.
• supplementary design of 7-(20,10,170) (# 8630) with respect to smaller t
• $PSL(2,19)$ 7 isomorphism types

---

# 8621: 7-(20,10,116)

• clan: 7-(20,10,116)
• Alltop construction for design 6-(19,9,116) (# 8618)
• $ {\bf PSL(2,19)}$ (3 isom. types) \cite{Bettenetal97b}

---

# 8622: 6-(19,10,290)

• clan: 7-(20,10,116), 1 times residual
• complementary design of 6-(19,9,116) (# 8618)
• residual design of 7-(20,10,116) (# 8621)
• residual design of supplementary of 7-(20,10,170) (# 8630)

---

# 8623: 5-(18,8,170)

• clan: 7-(20,10,170), 2 times derived
• derived from supplementary of 6-(19,9,116) (# 8618)
• derived from 6-(19,9,170) (# 8626)

---

# 8624: 5-(18,9,425)

• clan: 7-(20,10,170), 1 times derived, 1 times residual
• residual design of supplementary of 6-(19,9,116) (# 8618)
• derived from supplementary of 6-(19,10,290) (# 8622)
• residual design of 6-(19,9,170) (# 8626)
• derived from 6-(19,10,425) (# 8627)

---

# 8625: 6-(20,10,595)

• clan: 7-(20,10,170), 1 times reduced t
• supplementary design of 7-(20,10,116) (# 8621) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(19,9,170) (# 8626)
• Tran van Trung construction (right) for 6-(19,9,170) (# 8626) : der= 6-(19,9,170) and res= 6-(19,10,425) - the given design is the derived.
• Tran van Trung construction (left) for 6-(19,10,425) (# 8627) : der= 6-(19,9,170) and res= 6-(19,10,425) - the given design is the residual.
• design 7-(20,10,170) (# 8630) with respect to smaller t

---

# 8626: 6-(19,9,170)

• clan: 7-(20,10,170), 1 times derived
• derived from supplementary of 7-(20,10,116) (# 8621)
• derived from 7-(20,10,170) (# 8630)

---

# 8627: 6-(19,10,425)

• clan: 7-(20,10,170), 1 times residual
• residual design of supplementary of 7-(20,10,116) (# 8621)
• complementary design of 6-(19,9,170) (# 8626)
• residual design of 7-(20,10,170) (# 8630)

---

# 8628: 5-(18,10,522)

• clan: 7-(20,10,116), 2 times residual
• residual design of 6-(19,10,290) (# 8622)
• residual design of supplementary of 6-(19,10,425) (# 8627)

---

# 8629: 5-(18,10,765)

• clan: 7-(20,10,170), 2 times residual
• residual design of supplementary of 6-(19,10,290) (# 8622)
• residual design of 6-(19,10,425) (# 8627)

---

# 8630: 7-(20,10,170)

• clan: 7-(20,10,170)
• Alltop construction for design 6-(19,9,170) (# 8626)

---

# 8631: 6-(19,9,124)

• clan: 7-(20,10,124), 1 times derived
• $(ASL(2,9)\times Id_2)+$ ($\ge 12$ solutions)
• derived from 7-(20,10,124) (# 8633)
• derived from supplementary of 7-(20,10,162) (# 8642)

---

# 8632: 6-(20,10,434)

• clan: 7-(20,10,124), 1 times reduced t
• Tran van Trung construction with complementary design for 6-(19,9,124) (# 8631)
• Tran van Trung construction (right) for 6-(19,9,124) (# 8631) : der= 6-(19,9,124) and res= 6-(19,10,310) - the given design is the derived.
• design 7-(20,10,124) (# 8633) with respect to smaller t
• Tran van Trung construction (left) for 6-(19,10,310) (# 8634) : der= 6-(19,9,124) and res= 6-(19,10,310) - the given design is the residual.
• supplementary design of 7-(20,10,162) (# 8642) with respect to smaller t
• $PSL(2,19)$ 1 isomorphism type

---

# 8633: 7-(20,10,124)

• clan: 7-(20,10,124)
• Alltop construction for design 6-(19,9,124) (# 8631)
• $ {\bf PSL(2,19)}$ (1 isom. type) \cite{Bettenetal97b}

---

# 8634: 6-(19,10,310)

• clan: 7-(20,10,124), 1 times residual
• complementary design of 6-(19,9,124) (# 8631)
• residual design of 7-(20,10,124) (# 8633)
• residual design of supplementary of 7-(20,10,162) (# 8642)

---

# 8635: 5-(18,8,162)

• clan: 7-(20,10,162), 2 times derived
• derived from supplementary of 6-(19,9,124) (# 8631)
• derived from 6-(19,9,162) (# 8638)

---

# 8636: 5-(18,9,405)

• clan: 7-(20,10,162), 1 times derived, 1 times residual
• residual design of supplementary of 6-(19,9,124) (# 8631)
• derived from supplementary of 6-(19,10,310) (# 8634)
• residual design of 6-(19,9,162) (# 8638)
• derived from 6-(19,10,405) (# 8639)

---

# 8637: 6-(20,10,567)

• clan: 7-(20,10,162), 1 times reduced t
• supplementary design of 7-(20,10,124) (# 8633) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(19,9,162) (# 8638)
• Tran van Trung construction (right) for 6-(19,9,162) (# 8638) : der= 6-(19,9,162) and res= 6-(19,10,405) - the given design is the derived.
• Tran van Trung construction (left) for 6-(19,10,405) (# 8639) : der= 6-(19,9,162) and res= 6-(19,10,405) - the given design is the residual.
• design 7-(20,10,162) (# 8642) with respect to smaller t

---

# 8638: 6-(19,9,162)

• clan: 7-(20,10,162), 1 times derived
• derived from supplementary of 7-(20,10,124) (# 8633)
• derived from 7-(20,10,162) (# 8642)

---

# 8639: 6-(19,10,405)

• clan: 7-(20,10,162), 1 times residual
• residual design of supplementary of 7-(20,10,124) (# 8633)
• complementary design of 6-(19,9,162) (# 8638)
• residual design of 7-(20,10,162) (# 8642)

---

# 8640: 5-(18,10,558)

• clan: 7-(20,10,124), 2 times residual
• residual design of 6-(19,10,310) (# 8634)
• residual design of supplementary of 6-(19,10,405) (# 8639)

---

# 8641: 5-(18,10,729)

• clan: 7-(20,10,162), 2 times residual
• residual design of supplementary of 6-(19,10,310) (# 8634)
• residual design of 6-(19,10,405) (# 8639)

---

# 8642: 7-(20,10,162)

• clan: 7-(20,10,162)
• Alltop construction for design 6-(19,9,162) (# 8638)

---

# 8643: 6-(19,9,126)

• clan: 7-(20,10,126), 1 times derived
• $(PSL(2,8)\times C_2)+$ (24 solutions)
• derived from 7-(20,10,126) (# 8645)
• derived from supplementary of 7-(20,10,160) (# 8654)

---

# 8644: 6-(20,10,441)

• clan: 7-(20,10,126), 1 times reduced t
• Tran van Trung construction with complementary design for 6-(19,9,126) (# 8643)
• Tran van Trung construction (right) for 6-(19,9,126) (# 8643) : der= 6-(19,9,126) and res= 6-(19,10,315) - the given design is the derived.
• design 7-(20,10,126) (# 8645) with respect to smaller t
• Tran van Trung construction (left) for 6-(19,10,315) (# 8646) : der= 6-(19,9,126) and res= 6-(19,10,315) - the given design is the residual.
• supplementary design of 7-(20,10,160) (# 8654) with respect to smaller t
• $PSL(2,19)$ 4 isomorphism types

---

# 8645: 7-(20,10,126)

• clan: 7-(20,10,126)
• Alltop construction for design 6-(19,9,126) (# 8643)
• $(PGL(2,8)\times C_2)++$ (24 solutions, 4 isomorphism types)

---

# 8646: 6-(19,10,315)

• clan: 7-(20,10,126), 1 times residual
• complementary design of 6-(19,9,126) (# 8643)
• residual design of 7-(20,10,126) (# 8645)
• residual design of supplementary of 7-(20,10,160) (# 8654)

---

# 8647: 5-(18,8,160)

• clan: 7-(20,10,160), 2 times derived
• derived from supplementary of 6-(19,9,126) (# 8643)
• derived from 6-(19,9,160) (# 8650)

---

# 8648: 5-(18,9,400)

• clan: 7-(20,10,160), 1 times derived, 1 times residual
• residual design of supplementary of 6-(19,9,126) (# 8643)
• derived from supplementary of 6-(19,10,315) (# 8646)
• residual design of 6-(19,9,160) (# 8650)
• derived from 6-(19,10,400) (# 8651)

---

# 8649: 6-(20,10,560)

• clan: 7-(20,10,160), 1 times reduced t
• supplementary design of 7-(20,10,126) (# 8645) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(19,9,160) (# 8650)
• Tran van Trung construction (right) for 6-(19,9,160) (# 8650) : der= 6-(19,9,160) and res= 6-(19,10,400) - the given design is the derived.
• Tran van Trung construction (left) for 6-(19,10,400) (# 8651) : der= 6-(19,9,160) and res= 6-(19,10,400) - the given design is the residual.
• design 7-(20,10,160) (# 8654) with respect to smaller t

---

# 8650: 6-(19,9,160)

• clan: 7-(20,10,160), 1 times derived
• derived from supplementary of 7-(20,10,126) (# 8645)
• derived from 7-(20,10,160) (# 8654)

---

# 8651: 6-(19,10,400)

• clan: 7-(20,10,160), 1 times residual
• residual design of supplementary of 7-(20,10,126) (# 8645)
• complementary design of 6-(19,9,160) (# 8650)
• residual design of 7-(20,10,160) (# 8654)

---

# 8652: 5-(18,10,567)

• clan: 7-(20,10,126), 2 times residual
• residual design of 6-(19,10,315) (# 8646)
• residual design of supplementary of 6-(19,10,400) (# 8651)

---

# 8653: 5-(18,10,720)

• clan: 7-(20,10,160), 2 times residual
• residual design of supplementary of 6-(19,10,315) (# 8646)
• residual design of 6-(19,10,400) (# 8651)

---

# 8654: 7-(20,10,160)

• clan: 7-(20,10,160)
• Alltop construction for design 6-(19,9,160) (# 8650)

---

# 8655: 6-(20,10,336)

• clan: 7-(20,10,96), 1 times reduced t
• $PSL(3,4)-$ > 4101695 solutions

---

# 8656: 6-(20,10,469)

• clan: 7-(20,10,134), 1 times reduced t
• $PSL(2,19)$ 56 isomorphism types
• design 7-(20,10,134) (# 13115) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(19,9,134) (# 13116)
• Tran van Trung construction (right) for 6-(19,9,134) (# 13116) : der= 6-(19,9,134) and res= 6-(19,10,335) - the given design is the derived.
• Tran van Trung construction (left) for 6-(19,10,335) (# 13117) : der= 6-(19,9,134) and res= 6-(19,10,335) - the given design is the residual.
• supplementary design of 7-(20,10,152) (# 13126) with respect to smaller t

---

# 8657: 6-(20,10,476)

• clan: 7-(20,10,136), 1 times reduced t
• $PSL(3,4)-$ many isomorphism types

---

# 8658: 6-(20,8,28)

• clan: 11-(24,12,4), 1 times reduced t, 4 times derived
• $Id_2\times PSL(2,9)$ $\ge 16$ isomorphism types

---

# 8659: 5-(20,8,315)

• clan: 11-(24,12,9), 2 times reduced t, 4 times derived
• supplementary design of 6-(20,8,28) (# 8658) with respect to smaller t
• Tran van Trung construction (left) for 5-(19,8,252) (# 8660) : der= 5-(19,7,63) and res= 5-(19,8,252) - the given design is the residual.
• derived from supplementary of 6-(21,9,140) (# 8670)

---

# 8660: 5-(19,8,252)

• clan: 11-(24,12,9), 1 times reduced t, 4 times derived, 1 times residual
• residual design of supplementary of 6-(20,8,28) (# 8658)
• derived from supplementary of 6-(20,9,112) (# 8669)

---

# 8661: 5-(20,9,945)

• clan: 11-(24,12,9), 2 times reduced t, 3 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(19,8,252) (# 8660) : der= 5-(19,8,252) and res= 5-(19,9,693) - the given design is the derived.
• supplementary design of 6-(20,9,112) (# 8669) with respect to smaller t
• residual design of supplementary of 6-(21,9,140) (# 8670)

---

# 8662: 5-(21,9,1260)

• clan: 11-(24,12,9), 3 times reduced t, 3 times derived
• Tran van Trung construction (left) for 5-(20,9,945) (# 8661) : der= 5-(20,8,315) and res= 5-(20,9,945) - the given design is the residual.
• supplementary design of 6-(21,9,140) (# 8670) with respect to smaller t

---

# 8663: 5-(21,10,3024)

• clan: 11-(24,12,9), 3 times reduced t, 2 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(20,9,945) (# 8661) : der= 5-(20,9,945) and res= 5-(20,10,2079) - the given design is the derived.

---

# 8664: 5-(22,10,4284)

• clan: 11-(24,12,9), 4 times reduced t, 2 times derived
• Tran van Trung construction (right) for 5-(21,9,1260) (# 8662) : der= 5-(21,9,1260) and res= 5-(21,10,3024) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,10,3024) (# 8663) : der= 5-(21,9,1260) and res= 5-(21,10,3024) - the given design is the residual.

---

# 8665: 5-(22,11,8568)

• clan: 11-(24,12,9), 4 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 5-(21,10,3024) (# 8663)
• Tran van Trung construction (right) for 5-(21,10,3024) (# 8663) : der= 5-(21,10,3024) and res= 5-(21,11,5544) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,11,5544) (# 8666) : der= 5-(21,10,3024) and res= 5-(21,11,5544) - the given design is the residual.

---

# 8666: 5-(21,11,5544)

• clan: 11-(24,12,9), 3 times reduced t, 1 times derived, 2 times residual
• complementary design of 5-(21,10,3024) (# 8663)

---

# 8667: 5-(23,11,12852)

• clan: 11-(24,12,9), 5 times reduced t, 1 times derived
• Tran van Trung construction (right) for 5-(22,10,4284) (# 8664) : der= 5-(22,10,4284) and res= 5-(22,11,8568) - the given design is the derived.
• Tran van Trung construction (left) for 5-(22,11,8568) (# 8665) : der= 5-(22,10,4284) and res= 5-(22,11,8568) - the given design is the residual.

---

# 8668: 5-(24,12,34884)

• clan: 11-(24,12,9), 6 times reduced t
• Tran van Trung construction with complementary design for 5-(23,11,12852) (# 8667)

---

# 8669: 6-(20,9,112)

• clan: 11-(24,12,4), 1 times reduced t, 3 times derived, 1 times residual
• $C_2\times PGL(2,9)$ 196 solutions
• $PSL(2,19)$ (2 isom. types) \cite{Krameretal85}

---

# 8670: 6-(21,9,140)

• clan: 11-(24,12,4), 2 times reduced t, 3 times derived
• Tran van Trung construction (left) for 6-(20,9,112) (# 8669) : der= 6-(20,8,28) and res= 6-(20,9,112) - the given design is the residual.

---

# 8671: 6-(21,10,525)

• clan: 11-(24,12,5), 2 times reduced t, 2 times derived, 1 times residual
• $PSL(3,4)-+$
• derived from 7-(22,11,525) (# 8673)
• derived from supplementary of 7-(22,11,840) (# 8684)

---

# 8672: 6-(22,11,1680)

• clan: 11-(24,12,5), 3 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 6-(21,10,525) (# 8671)
• Tran van Trung construction (right) for 6-(21,10,525) (# 8671) : der= 6-(21,10,525) and res= 6-(21,11,1155) - the given design is the derived.
• design 7-(22,11,525) (# 8673) with respect to smaller t
• Tran van Trung construction (left) for 6-(21,11,1155) (# 8674) : der= 6-(21,10,525) and res= 6-(21,11,1155) - the given design is the residual.
• supplementary design of 7-(22,11,840) (# 8684) with respect to smaller t

---

# 8673: 7-(22,11,525)

• clan: 11-(24,12,5), 2 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 6-(21,10,525) (# 8671)

---

# 8674: 6-(21,11,1155)

• clan: 11-(24,12,5), 2 times reduced t, 1 times derived, 2 times residual
• complementary design of 6-(21,10,525) (# 8671)
• residual design of 7-(22,11,525) (# 8673)
• residual design of supplementary of 7-(22,11,840) (# 8684)

---

# 8675: 5-(21,10,2688)

• clan: 11-(24,12,8), 3 times reduced t, 2 times derived, 1 times residual
• supplementary design of 6-(21,10,525) (# 8671) with respect to smaller t
• derived from supplementary of 6-(22,11,1680) (# 8672)
• Tran van Trung construction (right) for 5-(20,9,840) (# 8676) : der= 5-(20,9,840) and res= 5-(20,10,1848) - the given design is the derived.
• derived from 6-(22,11,2688) (# 8679)
• design 6-(21,10,840) (# 8680) with respect to smaller t

---

# 8676: 5-(20,9,840)

• clan: 11-(24,12,8), 2 times reduced t, 3 times derived, 1 times residual
• derived from supplementary of 6-(21,10,525) (# 8671)
• derived from 6-(21,10,840) (# 8680)

---

# 8677: 5-(22,11,7616)

• clan: 11-(24,12,8), 4 times reduced t, 1 times derived, 1 times residual
• supplementary design of 6-(22,11,1680) (# 8672) with respect to smaller t
• Tran van Trung construction with complementary design for 5-(21,10,2688) (# 8675)
• Tran van Trung construction (right) for 5-(21,10,2688) (# 8675) : der= 5-(21,10,2688) and res= 5-(21,11,4928) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,11,4928) (# 8678) : der= 5-(21,10,2688) and res= 5-(21,11,4928) - the given design is the residual.
• design 6-(22,11,2688) (# 8679) with respect to smaller t

---

# 8678: 5-(21,11,4928)

• clan: 11-(24,12,8), 3 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 6-(22,11,1680) (# 8672)
• supplementary design of 6-(21,11,1155) (# 8674) with respect to smaller t
• complementary design of 5-(21,10,2688) (# 8675)
• residual design of 6-(22,11,2688) (# 8679)
• design 6-(21,11,1848) (# 8681) with respect to smaller t
• Tran van Trung construction (left) for 5-(20,11,3080) (# 8683) : der= 5-(20,10,1848) and res= 5-(20,11,3080) - the given design is the residual.

---

# 8679: 6-(22,11,2688)

• clan: 11-(24,12,8), 3 times reduced t, 1 times derived, 1 times residual
• supplementary design of 7-(22,11,525) (# 8673) with respect to smaller t
• Tran van Trung construction with complementary design for 6-(21,10,840) (# 8680)
• Tran van Trung construction (right) for 6-(21,10,840) (# 8680) : der= 6-(21,10,840) and res= 6-(21,11,1848) - the given design is the derived.
• Tran van Trung construction (left) for 6-(21,11,1848) (# 8681) : der= 6-(21,10,840) and res= 6-(21,11,1848) - the given design is the residual.
• design 7-(22,11,840) (# 8684) with respect to smaller t

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# 8680: 6-(21,10,840)

• clan: 11-(24,12,8), 2 times reduced t, 2 times derived, 1 times residual
• derived from supplementary of 7-(22,11,525) (# 8673)
• derived from 7-(22,11,840) (# 8684)

---

# 8681: 6-(21,11,1848)

• clan: 11-(24,12,8), 2 times reduced t, 1 times derived, 2 times residual
• residual design of supplementary of 7-(22,11,525) (# 8673)
• complementary design of 6-(21,10,840) (# 8680)
• residual design of 7-(22,11,840) (# 8684)

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# 8682: 5-(20,11,1925)

• clan: 11-(24,12,5), 2 times reduced t, 1 times derived, 3 times residual
• residual design of 6-(21,11,1155) (# 8674)
• residual design of supplementary of 6-(21,11,1848) (# 8681)

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# 8683: 5-(20,11,3080)

• clan: 11-(24,12,8), 2 times reduced t, 1 times derived, 3 times residual
• residual design of supplementary of 6-(21,11,1155) (# 8674)
• residual design of 6-(21,11,1848) (# 8681)

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# 8684: 7-(22,11,840)

• clan: 11-(24,12,8), 2 times reduced t, 1 times derived, 1 times residual
• Alltop construction for design 6-(21,10,840) (# 8680)

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# 8685: 6-(22,10,350)

• clan: 8-(24,12,350), 2 times derived
• $PSL(2,19)++$

---

# 8686: 5-(22,10,1190)

• clan: 8-(24,12,350), 1 times reduced t, 2 times derived
• design 6-(22,10,350) (# 8685) with respect to smaller t
• Tran van Trung construction (right) for 5-(21,9,350) (# 8687) : der= 5-(21,9,350) and res= 5-(21,10,840) - the given design is the derived.
• derived from 6-(23,11,1190) (# 8727)
• derived from supplementary of 6-(23,11,4998) (# 8734)

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# 8687: 5-(21,9,350)

• clan: 8-(24,12,350), 3 times derived
• derived from 6-(22,10,350) (# 8685)

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# 8688: 5-(22,10,4998)

• clan: 8-(24,12,1470), 1 times reduced t, 2 times derived
• supplementary design of 6-(22,10,350) (# 8685) with respect to smaller t
• Tran van Trung construction (right) for 5-(21,9,1470) (# 8689) : der= 5-(21,9,1470) and res= 5-(21,10,3528) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,10,3528) (# 8690) : der= 5-(21,9,1470) and res= 5-(21,10,3528) - the given design is the residual.
• derived from supplementary of 6-(23,11,1190) (# 8727)
• derived from 6-(23,11,4998) (# 8734)

---

# 8689: 5-(21,9,1470)

• clan: 8-(24,12,1470), 3 times derived
• derived from supplementary of 6-(22,10,350) (# 8685)

---

# 8690: 5-(21,10,3528)

• clan: 8-(24,12,1470), 2 times derived, 1 times residual
• residual design of supplementary of 6-(22,10,350) (# 8685)
• derived from supplementary of 6-(22,11,840) (# 8726)

---

# 8691: 5-(23,11,3570)

• clan: 8-(24,12,350), 2 times reduced t, 1 times derived
• Tran van Trung construction (right) for 5-(22,10,1190) (# 8686) : der= 5-(22,10,1190) and res= 5-(22,11,2380) - the given design is the derived.
• design 6-(23,11,1190) (# 8727) with respect to smaller t
• derived from 6-(24,12,3570) (# 8728)
• derived from supplementary of 6-(24,12,14994) (# 8733)
• supplementary design of 6-(23,11,4998) (# 8734) with respect to smaller t

---

# 8692: 5-(22,11,9996)

• clan: 8-(24,12,1470), 1 times reduced t, 1 times derived, 1 times residual
• Tran van Trung construction with complementary design for 5-(21,10,3528) (# 8690)
• Tran van Trung construction (right) for 5-(21,10,3528) (# 8690) : der= 5-(21,10,3528) and res= 5-(21,11,6468) - the given design is the derived.
• Tran van Trung construction (left) for 5-(21,11,6468) (# 8693) : der= 5-(21,10,3528) and res= 5-(21,11,6468) - the given design is the residual.
• supplementary design of 6-(22,11,840) (# 8726) with respect to smaller t
• residual design of supplementary of 6-(23,11,1190) (# 8727)
• derived from supplementary of 6-(23,12,2380) (# 8732)
• residual design of 6-(23,11,4998) (# 8734)
• derived from 6-(23,12,9996) (# 8735)

---

# 8693: 5-(21,11,6468)

• clan: 8-(24,12,1470), 1 times derived, 2 times residual
• complementary design of 5-(21,10,3528) (# 8690)
• residual design of supplementary of 6-(22,11,840) (# 8726)

---

# 8694: 5-(23,11,14994)

• clan: 8-(24,12,1470), 2 times reduced t, 1 times derived
• Tran van Trung construction (left) for 5-(22,11,9996) (# 8692) : der= 5-(22,10,4998) and res= 5-(22,11,9996) - the given design is the residual.
• supplementary design of 6-(23,11,1190) (# 8727) with respect to smaller t
• derived from supplementary of 6-(24,12,3570) (# 8728)
• derived from 6-(24,12,14994) (# 8733)
• design 6-(23,11,4998) (# 8734) with respect to smaller t

---

# 8695: 5-(24,12,40698)

• clan: 8-(24,12,1470), 3 times reduced t
• Tran van Trung construction with complementary design for 5-(23,11,14994) (# 8694)
• supplementary design of 6-(24,12,3570) (# 8728) with respect to smaller t
• Tran van Trung construction (left) for 5-(23,12,25704) (# 8731) : der= 5-(23,11,14994) and res= 5-(23,12,25704) - the given design is the residual.
• design 6-(24,12,14994) (# 8733) with respect to smaller t

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# 8696: 6-(22,10,840)

• clan: 11-(24,12,6), 3 times reduced t, 2 times derived
• $PSL(2,19)++$

---

# 8697: 5-(22,10,3332)

• clan: 11-(24,12,7), 4 times reduced t, 2 times derived
• supplementary design of 6-(22,10,840) (# 8696) with respect to smaller t
• Tran van Trung construction (right) for 5-(21,9,980) (# 8698) : der= 5-(21,9,980) and res= 5-(21,10,2352) - the given design is the derived.
• derived from supplementary of 6-(23,11,2856) (# 8714)
• derived from 6-(23,11,3332) (# 8721)

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# 8698: 5-(21,9,980)

• clan: 11-(24,12,7), 3 times reduced t, 3 times derived
• derived from supplementary of 6-(22,10,840) (# 8696)

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# 8699: 5-(23,11,9996)

• clan: 11-(24,12,7), 5 times reduced t, 1 times derived
• Tran van Trung construction (right) for 5-(22,10,3332) (# 8697) : der= 5-(22,10,3332) and res= 5-(22,11,6664) - the given design is the derived.
• supplementary design of 6-(23,11,2856) (# 8714) with respect to smaller t
• derived from supplementary of 6-(24,12,8568) (# 8715)
• derived from 6-(24,12,9996) (# 8720)
• design 6-(23,11,3332) (# 8721) with respect to smaller t

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created: Fri Oct 23 11:12:04 CEST 2009