t designs with small t, id ge 12200

---

# 12200: 5-(30,10,44310)

• clan: 8-(31,10,211), 2 times reduced t, 1 times residual
• supplementary design of 6-(30,10,1764) (# 12197) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,35448) (# 12201) : der= 5-(29,9,8862) and res= 5-(29,10,35448) - the given design is the residual.
• residual design of supplementary of 6-(31,10,2100) (# 12202)

---

# 12201: 5-(29,10,35448)

• clan: 8-(31,10,211), 1 times reduced t, 2 times residual
• residual design of supplementary of 6-(30,10,1764) (# 12197)

---

# 12202: 6-(31,10,2100)

• clan: 8-(31,10,42), 2 times reduced t
• Tran van Trung construction (left) for 6-(30,10,1764) (# 12197) : der= 6-(30,9,336) and res= 6-(30,10,1764) - the given design is the residual.

---

# 12203: 5-(31,10,10920)

• clan: 8-(31,10,42), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,8820) (# 12198) : der= 5-(30,9,2100) and res= 5-(30,10,8820) - the given design is the residual.
• design 6-(31,10,2100) (# 12202) with respect to smaller t

---

# 12204: 5-(31,10,54860)

• clan: 8-(31,10,211), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,44310) (# 12200) : der= 5-(30,9,10550) and res= 5-(30,10,44310) - the given design is the residual.
• supplementary design of 6-(31,10,2100) (# 12202) with respect to smaller t

---

# 12205: 6-(30,10,2688)

• clan: 8-(31,10,64), 1 times reduced t, 1 times residual
• $P\Gamma L(2,27)++$ (many isom. types) \cite{Bettenetal97b}

---

# 12206: 5-(30,10,13440)

• clan: 8-(31,10,64), 2 times reduced t, 1 times residual
• design 6-(30,10,2688) (# 12205) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,10752) (# 12207) : der= 5-(29,9,2688) and res= 5-(29,10,10752) - the given design is the residual.
• residual design of 6-(31,10,3200) (# 12210)

---

# 12207: 5-(29,10,10752)

• clan: 8-(31,10,64), 1 times reduced t, 2 times residual
• residual design of 6-(30,10,2688) (# 12205)

---

# 12208: 5-(30,10,39690)

• clan: 8-(31,10,189), 2 times reduced t, 1 times residual
• supplementary design of 6-(30,10,2688) (# 12205) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,31752) (# 12209) : der= 5-(29,9,7938) and res= 5-(29,10,31752) - the given design is the residual.
• residual design of supplementary of 6-(31,10,3200) (# 12210)

---

# 12209: 5-(29,10,31752)

• clan: 8-(31,10,189), 1 times reduced t, 2 times residual
• residual design of supplementary of 6-(30,10,2688) (# 12205)

---

# 12210: 6-(31,10,3200)

• clan: 8-(31,10,64), 2 times reduced t
• Tran van Trung construction (left) for 6-(30,10,2688) (# 12205) : der= 6-(30,9,512) and res= 6-(30,10,2688) - the given design is the residual.

---

# 12211: 5-(31,10,16640)

• clan: 8-(31,10,64), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,13440) (# 12206) : der= 5-(30,9,3200) and res= 5-(30,10,13440) - the given design is the residual.
• design 6-(31,10,3200) (# 12210) with respect to smaller t

---

# 12212: 5-(31,10,49140)

• clan: 8-(31,10,189), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,39690) (# 12208) : der= 5-(30,9,9450) and res= 5-(30,10,39690) - the given design is the residual.
• supplementary design of 6-(31,10,3200) (# 12210) with respect to smaller t

---

# 12213: 6-(30,10,2898)

• clan: 9-(31,10,6), 2 times reduced t, 1 times residual
• \cite{Sebille98} $P\Gamma L(2,27)\cup S_2$
• Tran van Trung construction (left) for 6-(29,10,2415) (# 15827) : der= 6-(29,9,483) and res= 6-(29,10,2415) - the given design is the residual.

---

# 12214: 5-(30,10,14490)

• clan: 9-(31,10,6), 3 times reduced t, 1 times residual
• design 6-(30,10,2898) (# 12213) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,11592) (# 12215) : der= 5-(29,9,2898) and res= 5-(29,10,11592) - the given design is the residual.
• residual design of 6-(31,10,3450) (# 12218)

---

# 12215: 5-(29,10,11592)

• clan: 9-(31,10,6), 2 times reduced t, 2 times residual
• residual design of 6-(30,10,2898) (# 12213)
• design 6-(29,10,2415) (# 15827) with respect to smaller t
• supplementary design of 6-(29,10,6440) (# 15830) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,10,9177) (# 15833) : der= 5-(28,9,2415) and res= 5-(28,10,9177) - the given design is the residual.

---

# 12216: 5-(30,10,38640)

• clan: 9-(31,10,16), 3 times reduced t, 1 times residual
• supplementary design of 6-(30,10,2898) (# 12213) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,30912) (# 12217) : der= 5-(29,9,7728) and res= 5-(29,10,30912) - the given design is the residual.
• residual design of supplementary of 6-(31,10,3450) (# 12218)

---

# 12217: 5-(29,10,30912)

• clan: 9-(31,10,16), 2 times reduced t, 2 times residual
• residual design of supplementary of 6-(30,10,2898) (# 12213)
• supplementary design of 6-(29,10,2415) (# 15827) with respect to smaller t
• design 6-(29,10,6440) (# 15830) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,10,24472) (# 15834) : der= 5-(28,9,6440) and res= 5-(28,10,24472) - the given design is the residual.

---

# 12218: 6-(31,10,3450)

• clan: 9-(31,10,6), 3 times reduced t
• Tran van Trung construction (left) for 6-(30,10,2898) (# 12213) : der= 6-(30,9,552) and res= 6-(30,10,2898) - the given design is the residual.

---

# 12219: 5-(31,10,17940)

• clan: 9-(31,10,6), 4 times reduced t
• Tran van Trung construction (left) for 5-(30,10,14490) (# 12214) : der= 5-(30,9,3450) and res= 5-(30,10,14490) - the given design is the residual.
• design 6-(31,10,3450) (# 12218) with respect to smaller t

---

# 12220: 5-(31,10,47840)

• clan: 9-(31,10,16), 4 times reduced t
• Tran van Trung construction (left) for 5-(30,10,38640) (# 12216) : der= 5-(30,9,9200) and res= 5-(30,10,38640) - the given design is the residual.
• supplementary design of 6-(31,10,3450) (# 12218) with respect to smaller t

---

# 12221: 6-(30,10,3570)

• clan: 8-(31,10,85), 1 times reduced t, 1 times residual
• $P\Gamma L(2,27)++$ (many isom. types) \cite{Bettenetal97b}

---

# 12222: 5-(30,10,17850)

• clan: 8-(31,10,85), 2 times reduced t, 1 times residual
• design 6-(30,10,3570) (# 12221) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,14280) (# 12223) : der= 5-(29,9,3570) and res= 5-(29,10,14280) - the given design is the residual.
• residual design of 6-(31,10,4250) (# 12226)

---

# 12223: 5-(29,10,14280)

• clan: 8-(31,10,85), 1 times reduced t, 2 times residual
• residual design of 6-(30,10,3570) (# 12221)

---

# 12224: 5-(30,10,35280)

• clan: 8-(31,10,168), 2 times reduced t, 1 times residual
• supplementary design of 6-(30,10,3570) (# 12221) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,28224) (# 12225) : der= 5-(29,9,7056) and res= 5-(29,10,28224) - the given design is the residual.
• residual design of supplementary of 6-(31,10,4250) (# 12226)

---

# 12225: 5-(29,10,28224)

• clan: 8-(31,10,168), 1 times reduced t, 2 times residual
• residual design of supplementary of 6-(30,10,3570) (# 12221)

---

# 12226: 6-(31,10,4250)

• clan: 8-(31,10,85), 2 times reduced t
• Tran van Trung construction (left) for 6-(30,10,3570) (# 12221) : der= 6-(30,9,680) and res= 6-(30,10,3570) - the given design is the residual.

---

# 12227: 5-(31,10,22100)

• clan: 8-(31,10,85), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,17850) (# 12222) : der= 5-(30,9,4250) and res= 5-(30,10,17850) - the given design is the residual.
• design 6-(31,10,4250) (# 12226) with respect to smaller t

---

# 12228: 5-(31,10,43680)

• clan: 8-(31,10,168), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,35280) (# 12224) : der= 5-(30,9,8400) and res= 5-(30,10,35280) - the given design is the residual.
• supplementary design of 6-(31,10,4250) (# 12226) with respect to smaller t

---

# 12229: 6-(30,10,4158)

• clan: 21-(44,22,9), 1 times reduced t, 12 times derived, 2 times residual
• $P\Gamma L(2,27)++$ (many >= 404 isom. types) \cite{Bettenetal97b}
• design 7-(30,10,693) (# 15987) with respect to smaller t
• Tran van Trung construction (left) for 6-(29,10,3465) (# 15988) : der= 6-(29,9,693) and res= 6-(29,10,3465) - the given design is the residual.

---

# 12230: 5-(30,10,20790)

• clan: 21-(44,22,9), 2 times reduced t, 12 times derived, 2 times residual
• design 6-(30,10,4158) (# 12229) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,16632) (# 12231) : der= 5-(29,9,4158) and res= 5-(29,10,16632) - the given design is the residual.
• residual design of 6-(31,10,4950) (# 12234)
• supplementary design of 6-(30,10,6468) (# 15989) with respect to smaller t

---

# 12231: 5-(29,10,16632)

• clan: 21-(44,22,9), 1 times reduced t, 12 times derived, 3 times residual
• residual design of 6-(30,10,4158) (# 12229)
• design 6-(29,10,3465) (# 15988) with respect to smaller t
• residual design of supplementary of 6-(30,10,6468) (# 15989)
• supplementary design of 6-(29,10,5390) (# 15991) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,10,13167) (# 15992) : der= 5-(28,9,3465) and res= 5-(28,10,13167) - the given design is the residual.

---

# 12232: 5-(30,10,32340)

• clan: 21-(44,22,14), 2 times reduced t, 12 times derived, 2 times residual
• supplementary design of 6-(30,10,4158) (# 12229) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,25872) (# 12233) : der= 5-(29,9,6468) and res= 5-(29,10,25872) - the given design is the residual.
• residual design of supplementary of 6-(31,10,4950) (# 12234)
• design 6-(30,10,6468) (# 15989) with respect to smaller t

---

# 12233: 5-(29,10,25872)

• clan: 21-(44,22,14), 1 times reduced t, 12 times derived, 3 times residual
• residual design of supplementary of 6-(30,10,4158) (# 12229)
• supplementary design of 6-(29,10,3465) (# 15988) with respect to smaller t
• residual design of 6-(30,10,6468) (# 15989)
• design 6-(29,10,5390) (# 15991) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,10,20482) (# 15993) : der= 5-(28,9,5390) and res= 5-(28,10,20482) - the given design is the residual.

---

# 12234: 6-(31,10,4950)

• clan: 21-(44,22,9), 2 times reduced t, 12 times derived, 1 times residual
• Tran van Trung construction (left) for 6-(30,10,4158) (# 12229) : der= 6-(30,9,792) and res= 6-(30,10,4158) - the given design is the residual.

---

# 12235: 5-(31,10,25740)

• clan: 21-(44,22,9), 3 times reduced t, 12 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(30,10,20790) (# 12230) : der= 5-(30,9,4950) and res= 5-(30,10,20790) - the given design is the residual.
• design 6-(31,10,4950) (# 12234) with respect to smaller t
• residual design of 6-(32,10,5850) (# 12287)

---

# 12236: 5-(31,10,40040)

• clan: 21-(44,22,14), 3 times reduced t, 12 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(30,10,32340) (# 12232) : der= 5-(30,9,7700) and res= 5-(30,10,32340) - the given design is the residual.
• supplementary design of 6-(31,10,4950) (# 12234) with respect to smaller t
• residual design of supplementary of 6-(32,10,5850) (# 12287)

---

# 12237: 5-(32,10,31590)

• clan: 21-(44,22,9), 4 times reduced t, 12 times derived
• Tran van Trung construction (left) for 5-(31,10,25740) (# 12235) : der= 5-(31,9,5850) and res= 5-(31,10,25740) - the given design is the residual.
• design 6-(32,10,5850) (# 12287) with respect to smaller t

---

# 12238: 6-(30,10,4410)

• clan: 8-(31,10,105), 1 times reduced t, 1 times residual
• $P\Gamma L(2,27)++$ (many >= 8300 isom. types) \cite{Bettenetal97b}
• design 7-(30,10,735) (# 15994) with respect to smaller t
• Tran van Trung construction (left) for 6-(29,10,3675) (# 15995) : der= 6-(29,9,735) and res= 6-(29,10,3675) - the given design is the residual.
• residual design of 7-(31,10,840) (# 16049)

---

# 12239: 5-(30,10,22050)

• clan: 8-(31,10,105), 2 times reduced t, 1 times residual
• design 6-(30,10,4410) (# 12238) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,17640) (# 12240) : der= 5-(29,9,4410) and res= 5-(29,10,17640) - the given design is the residual.
• residual design of 6-(31,10,5250) (# 12243)
• supplementary design of 6-(30,10,6216) (# 15996) with respect to smaller t
• residual design of supplementary of 6-(31,10,7400) (# 16050)

---

# 12240: 5-(29,10,17640)

• clan: 8-(31,10,105), 1 times reduced t, 2 times residual
• residual design of 6-(30,10,4410) (# 12238)
• design 6-(29,10,3675) (# 15995) with respect to smaller t
• residual design of supplementary of 6-(30,10,6216) (# 15996)
• supplementary design of 6-(29,10,5180) (# 15998) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,10,13965) (# 15999) : der= 5-(28,9,3675) and res= 5-(28,10,13965) - the given design is the residual.

---

# 12241: 5-(30,10,31080)

• clan: 8-(31,10,148), 2 times reduced t, 1 times residual
• supplementary design of 6-(30,10,4410) (# 12238) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,24864) (# 12242) : der= 5-(29,9,6216) and res= 5-(29,10,24864) - the given design is the residual.
• residual design of supplementary of 6-(31,10,5250) (# 12243)
• design 6-(30,10,6216) (# 15996) with respect to smaller t
• residual design of 6-(31,10,7400) (# 16050)

---

# 12242: 5-(29,10,24864)

• clan: 8-(31,10,148), 1 times reduced t, 2 times residual
• residual design of supplementary of 6-(30,10,4410) (# 12238)
• supplementary design of 6-(29,10,3675) (# 15995) with respect to smaller t
• residual design of 6-(30,10,6216) (# 15996)
• design 6-(29,10,5180) (# 15998) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,10,19684) (# 16000) : der= 5-(28,9,5180) and res= 5-(28,10,19684) - the given design is the residual.

---

# 12243: 6-(31,10,5250)

• clan: 8-(31,10,105), 2 times reduced t
• Tran van Trung construction (left) for 6-(30,10,4410) (# 12238) : der= 6-(30,9,840) and res= 6-(30,10,4410) - the given design is the residual.
• design 7-(31,10,840) (# 16049) with respect to smaller t

---

# 12244: 5-(31,10,27300)

• clan: 8-(31,10,105), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,22050) (# 12239) : der= 5-(30,9,5250) and res= 5-(30,10,22050) - the given design is the residual.
• design 6-(31,10,5250) (# 12243) with respect to smaller t
• supplementary design of 6-(31,10,7400) (# 16050) with respect to smaller t

---

# 12245: 5-(31,10,38480)

• clan: 8-(31,10,148), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,31080) (# 12241) : der= 5-(30,9,7400) and res= 5-(30,10,31080) - the given design is the residual.
• supplementary design of 6-(31,10,5250) (# 12243) with respect to smaller t
• design 6-(31,10,7400) (# 16050) with respect to smaller t

---

# 12246: 6-(30,10,4704)

• clan: 8-(31,10,112), 1 times reduced t, 1 times residual
• $P\Gamma L(2,27)++$ (many isom. types) \cite{Bettenetal97b}

---

# 12247: 5-(30,10,23520)

• clan: 8-(31,10,112), 2 times reduced t, 1 times residual
• design 6-(30,10,4704) (# 12246) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,18816) (# 12248) : der= 5-(29,9,4704) and res= 5-(29,10,18816) - the given design is the residual.
• residual design of 6-(31,10,5600) (# 12251)

---

# 12248: 5-(29,10,18816)

• clan: 8-(31,10,112), 1 times reduced t, 2 times residual
• residual design of 6-(30,10,4704) (# 12246)

---

# 12249: 5-(30,10,29610)

• clan: 8-(31,10,141), 2 times reduced t, 1 times residual
• supplementary design of 6-(30,10,4704) (# 12246) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,23688) (# 12250) : der= 5-(29,9,5922) and res= 5-(29,10,23688) - the given design is the residual.
• residual design of supplementary of 6-(31,10,5600) (# 12251)

---

# 12250: 5-(29,10,23688)

• clan: 8-(31,10,141), 1 times reduced t, 2 times residual
• residual design of supplementary of 6-(30,10,4704) (# 12246)

---

# 12251: 6-(31,10,5600)

• clan: 8-(31,10,112), 2 times reduced t
• Tran van Trung construction (left) for 6-(30,10,4704) (# 12246) : der= 6-(30,9,896) and res= 6-(30,10,4704) - the given design is the residual.

---

# 12252: 5-(31,10,29120)

• clan: 8-(31,10,112), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,23520) (# 12247) : der= 5-(30,9,5600) and res= 5-(30,10,23520) - the given design is the residual.
• design 6-(31,10,5600) (# 12251) with respect to smaller t

---

# 12253: 5-(31,10,36660)

• clan: 8-(31,10,141), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,29610) (# 12249) : der= 5-(30,9,7050) and res= 5-(30,10,29610) - the given design is the residual.
• supplementary design of 6-(31,10,5600) (# 12251) with respect to smaller t

---

# 12254: 6-(30,10,4956)

• clan: 8-(31,10,118), 1 times reduced t, 1 times residual
• $P\Gamma L(2,27)++$ \cite{Bettenetal97b}

---

# 12255: 5-(30,10,24780)

• clan: 8-(31,10,118), 2 times reduced t, 1 times residual
• design 6-(30,10,4956) (# 12254) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,19824) (# 12256) : der= 5-(29,9,4956) and res= 5-(29,10,19824) - the given design is the residual.

---

# 12256: 5-(29,10,19824)

• clan: 8-(31,10,118), 1 times reduced t, 2 times residual
• residual design of 6-(30,10,4956) (# 12254)

---

# 12257: 5-(30,10,28350)

• clan: 8-(31,10,135), 2 times reduced t, 1 times residual
• supplementary design of 6-(30,10,4956) (# 12254) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,22680) (# 12258) : der= 5-(29,9,5670) and res= 5-(29,10,22680) - the given design is the residual.

---

# 12258: 5-(29,10,22680)

• clan: 8-(31,10,135), 1 times reduced t, 2 times residual
• residual design of supplementary of 6-(30,10,4956) (# 12254)

---

# 12259: 6-(30,10,5082)

• clan: 21-(44,22,11), 1 times reduced t, 12 times derived, 2 times residual
• $P\Gamma L(2,27)++$ \cite{Bettenetal97b}
• design 7-(30,10,847) (# 16033) with respect to smaller t
• Tran van Trung construction (right) for 6-(29,9,847) (# 16034) : der= 6-(29,9,847) and res= 6-(29,10,4235) - the given design is the derived.
• Tran van Trung construction (left) for 6-(29,10,4235) (# 16035) : der= 6-(29,9,847) and res= 6-(29,10,4235) - the given design is the residual.

---

# 12260: 5-(30,10,25410)

• clan: 21-(44,22,11), 2 times reduced t, 12 times derived, 2 times residual
• design 6-(30,10,5082) (# 12259) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,20328) (# 12261) : der= 5-(29,9,5082) and res= 5-(29,10,20328) - the given design is the residual.
• supplementary design of 6-(30,10,5544) (# 16036) with respect to smaller t

---

# 12261: 5-(29,10,20328)

• clan: 21-(44,22,11), 1 times reduced t, 12 times derived, 3 times residual
• residual design of 6-(30,10,5082) (# 12259)
• design 6-(29,10,4235) (# 16035) with respect to smaller t
• residual design of supplementary of 6-(30,10,5544) (# 16036)
• supplementary design of 6-(29,10,4620) (# 16038) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,10,16093) (# 16040) : der= 5-(28,9,4235) and res= 5-(28,10,16093) - the given design is the residual.

---

# 12262: 5-(30,10,27720)

• clan: 21-(44,22,12), 2 times reduced t, 12 times derived, 2 times residual
• supplementary design of 6-(30,10,5082) (# 12259) with respect to smaller t
• Tran van Trung construction (right) for 5-(29,9,5544) (# 12263) : der= 5-(29,9,5544) and res= 5-(29,10,22176) - the given design is the derived.
• Tran van Trung construction (left) for 5-(29,10,22176) (# 12264) : der= 5-(29,9,5544) and res= 5-(29,10,22176) - the given design is the residual.
• design 6-(30,10,5544) (# 16036) with respect to smaller t

---

# 12263: 5-(29,9,5544)

• clan: 21-(44,22,12), 1 times reduced t, 13 times derived, 2 times residual
• derived from supplementary of 6-(30,10,5082) (# 12259)
• supplementary design of 6-(29,9,847) (# 16034) with respect to smaller t
• derived from 6-(30,10,5544) (# 16036)
• design 6-(29,9,924) (# 16037) with respect to smaller t
• Tran van Trung construction (left) for 5-(28,9,4620) (# 16039) : der= 5-(28,8,924) and res= 5-(28,9,4620) - the given design is the residual.

---

# 12264: 5-(29,10,22176)

• clan: 21-(44,22,12), 1 times reduced t, 12 times derived, 3 times residual
• residual design of supplementary of 6-(30,10,5082) (# 12259)
• supplementary design of 6-(29,10,4235) (# 16035) with respect to smaller t
• residual design of 6-(30,10,5544) (# 16036)
• design 6-(29,10,4620) (# 16038) with respect to smaller t
• Tran van Trung construction (right) for 5-(28,9,4620) (# 16039) : der= 5-(28,9,4620) and res= 5-(28,10,17556) - the given design is the derived.
• Tran van Trung construction (left) for 5-(28,10,17556) (# 16041) : der= 5-(28,9,4620) and res= 5-(28,10,17556) - the given design is the residual.

---

# 12265: 5-(31,10,31460)

• clan: 21-(44,22,11), 3 times reduced t, 12 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(30,10,25410) (# 12260) : der= 5-(30,9,6050) and res= 5-(30,10,25410) - the given design is the residual.

---

# 12266: 5-(30,9,6600)

• clan: 21-(44,22,12), 2 times reduced t, 13 times derived, 1 times residual
• Tran van Trung construction (left) for 5-(29,9,5544) (# 12263) : der= 5-(29,8,1056) and res= 5-(29,9,5544) - the given design is the residual.

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# 12267: 5-(32,10,38610)

• clan: 21-(44,22,11), 4 times reduced t, 12 times derived
• Tran van Trung construction (left) for 5-(31,10,31460) (# 12265) : der= 5-(31,9,7150) and res= 5-(31,10,31460) - the given design is the residual.

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# 12268: 5-(31,9,7800)

• clan: 21-(44,22,12), 3 times reduced t, 13 times derived
• Tran van Trung construction (left) for 5-(30,9,6600) (# 12266) : der= 5-(30,8,1200) and res= 5-(30,9,6600) - the given design is the residual.

---

# 12269: 5-(31,10,34320)

• clan: 21-(44,22,12), 3 times reduced t, 12 times derived, 1 times residual
• Tran van Trung construction (right) for 5-(30,9,6600) (# 12266) : der= 5-(30,9,6600) and res= 5-(30,10,27720) - the given design is the derived.

---

# 12270: 5-(32,10,42120)

• clan: 21-(44,22,12), 4 times reduced t, 12 times derived
• Tran van Trung construction (right) for 5-(31,9,7800) (# 12268) : der= 5-(31,9,7800) and res= 5-(31,10,34320) - the given design is the derived.
• Tran van Trung construction (left) for 5-(31,10,34320) (# 12269) : der= 5-(31,9,7800) and res= 5-(31,10,34320) - the given design is the residual.

---

# 12271: 6-(30,10,5292)

• clan: 8-(31,10,126), 1 times reduced t, 1 times residual
• $P\Gamma L(2,27)++$ (>= 4970 isom. types) \cite{Bettenetal97b}

---

# 12272: 5-(30,10,26460)

• clan: 8-(31,10,126), 2 times reduced t, 1 times residual
• design 6-(30,10,5292) (# 12271) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,21168) (# 12273) : der= 5-(29,9,5292) and res= 5-(29,10,21168) - the given design is the residual.
• residual design of 6-(31,10,6300) (# 12276)

---

# 12273: 5-(29,10,21168)

• clan: 8-(31,10,126), 1 times reduced t, 2 times residual
• residual design of 6-(30,10,5292) (# 12271)

---

# 12274: 5-(30,10,26670)

• clan: 8-(31,10,127), 2 times reduced t, 1 times residual
• supplementary design of 6-(30,10,5292) (# 12271) with respect to smaller t
• Tran van Trung construction (left) for 5-(29,10,21336) (# 12275) : der= 5-(29,9,5334) and res= 5-(29,10,21336) - the given design is the residual.
• residual design of supplementary of 6-(31,10,6300) (# 12276)

---

# 12275: 5-(29,10,21336)

• clan: 8-(31,10,127), 1 times reduced t, 2 times residual
• residual design of supplementary of 6-(30,10,5292) (# 12271)

---

# 12276: 6-(31,10,6300)

• clan: 8-(31,10,126), 2 times reduced t
• Tran van Trung construction (left) for 6-(30,10,5292) (# 12271) : der= 6-(30,9,1008) and res= 6-(30,10,5292) - the given design is the residual.

---

# 12277: 5-(31,10,32760)

• clan: 8-(31,10,126), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,26460) (# 12272) : der= 5-(30,9,6300) and res= 5-(30,10,26460) - the given design is the residual.
• design 6-(31,10,6300) (# 12276) with respect to smaller t

---

# 12278: 5-(31,10,33020)

• clan: 8-(31,10,127), 3 times reduced t
• Tran van Trung construction (left) for 5-(30,10,26670) (# 12274) : der= 5-(30,9,6350) and res= 5-(30,10,26670) - the given design is the residual.
• supplementary design of 6-(31,10,6300) (# 12276) with respect to smaller t

---

# 12279: 6-(30,7,12)

• clan: 6-(30,7,12)
• $PSL(2,29)$ (many) (6-(8m+6,7,4m) for m=3 (\cite{Teirlinck89})), Halving of the complete design

---

# 12280: 5-(29,6,12)

• clan: 6-(30,7,12), 1 times derived
• derived from 6-(30,7,12) (# 12279)
• derived from supplementary of 6-(30,7,12) (# 12279)

---

# 12281: 5-(29,7,138)

• clan: 6-(30,7,12), 1 times residual
• residual design of 6-(30,7,12) (# 12279)
• residual design of supplementary of 6-(30,7,12) (# 12279)

---

# 12282: 6-(30,8,108)

• clan: 21-(44,22,9), 1 times reduced t, 14 times derived
• $PGGL(2,27)++$ (many isom. types)

---

# 12283: 5-(30,8,1400)

• clan: 21-(44,22,14), 2 times reduced t, 14 times derived
• supplementary design of 6-(30,8,108) (# 12282) with respect to smaller t
• Tran van Trung construction (right) for 5-(29,7,168) (# 12284) : der= 5-(29,7,168) and res= 5-(29,8,1232) - the given design is the derived.
• derived from supplementary of 6-(31,9,900) (# 12285)

---

# 12284: 5-(29,7,168)

• clan: 21-(44,22,14), 1 times reduced t, 15 times derived
• derived from supplementary of 6-(30,8,108) (# 12282)

---

# 12285: 6-(31,9,900)

• clan: 21-(44,22,9), 2 times reduced t, 13 times derived
• Tran van Trung construction (right) for 6-(30,8,108) (# 12282) : der= 6-(30,8,108) and res= 6-(30,9,792) - the given design is the derived.
• $P\Gamma L(2,27) + S_3$

---

# 12286: 5-(31,9,9100)

• clan: 21-(44,22,14), 3 times reduced t, 13 times derived
• Tran van Trung construction (right) for 5-(30,8,1400) (# 12283) : der= 5-(30,8,1400) and res= 5-(30,9,7700) - the given design is the derived.
• supplementary design of 6-(31,9,900) (# 12285) with respect to smaller t
• derived from supplementary of 6-(32,10,5850) (# 12287)

---

# 12287: 6-(32,10,5850)

• clan: 21-(44,22,9), 3 times reduced t, 12 times derived
• Tran van Trung construction (right) for 6-(31,9,900) (# 12285) : der= 6-(31,9,900) and res= 6-(31,10,4950) - the given design is the derived.

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# 12288: 5-(32,10,49140)

• clan: 21-(44,22,14), 4 times reduced t, 12 times derived
• Tran van Trung construction (right) for 5-(31,9,9100) (# 12286) : der= 5-(31,9,9100) and res= 5-(31,10,40040) - the given design is the derived.
• supplementary design of 6-(32,10,5850) (# 12287) with respect to smaller t

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# 12289: 6-(31,9,1040)

• clan: 19-(44,22,1040), 13 times derived
• $P\Gamma L(2,27) + S_3$

---

# 12290: 5-(31,9,6760)

• clan: 19-(44,22,1040), 1 times reduced t, 13 times derived
• design 6-(31,9,1040) (# 12289) with respect to smaller t
• Tran van Trung construction (right) for 5-(30,8,1040) (# 12291) : der= 5-(30,8,1040) and res= 5-(30,9,5720) - the given design is the derived.
• Tran van Trung construction (left) for 5-(30,9,5720) (# 12292) : der= 5-(30,8,1040) and res= 5-(30,9,5720) - the given design is the residual.

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# 12291: 5-(30,8,1040)

• clan: 19-(44,22,1040), 14 times derived
• derived from 6-(31,9,1040) (# 12289)

---

# 12292: 5-(30,9,5720)

• clan: 19-(44,22,1040), 13 times derived, 1 times residual
• residual design of 6-(31,9,1040) (# 12289)

---

# 12293: 5-(31,9,8190)

• clan: 19-(44,22,1260), 1 times reduced t, 13 times derived
• supplementary design of 6-(31,9,1040) (# 12289) with respect to smaller t
• Tran van Trung construction (right) for 5-(30,8,1260) (# 12294) : der= 5-(30,8,1260) and res= 5-(30,9,6930) - the given design is the derived.
• Tran van Trung construction (left) for 5-(30,9,6930) (# 12295) : der= 5-(30,8,1260) and res= 5-(30,9,6930) - the given design is the residual.

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# 12294: 5-(30,8,1260)

• clan: 19-(44,22,1260), 14 times derived
• derived from supplementary of 6-(31,9,1040) (# 12289)

---

# 12295: 5-(30,9,6930)

• clan: 19-(44,22,1260), 13 times derived, 1 times residual
• residual design of supplementary of 6-(31,9,1040) (# 12289)

---

# 12296: 6-(31,9,200)

• clan: 21-(44,22,2), 2 times reduced t, 13 times derived
• $P\Gamma L(2,27) + S_3$

---

# 12297: 5-(31,9,13650)

• clan: 21-(44,22,21), 3 times reduced t, 13 times derived
• supplementary design of 6-(31,9,200) (# 12296) with respect to smaller t
• Tran van Trung construction (right) for 5-(30,8,2100) (# 12298) : der= 5-(30,8,2100) and res= 5-(30,9,11550) - the given design is the derived.
• Tran van Trung construction (left) for 5-(30,9,11550) (# 12299) : der= 5-(30,8,2100) and res= 5-(30,9,11550) - the given design is the residual.

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# 12298: 5-(30,8,2100)

• clan: 21-(44,22,21), 2 times reduced t, 14 times derived
• derived from supplementary of 6-(31,9,200) (# 12296)

---

# 12299: 5-(30,9,11550)

• clan: 21-(44,22,21), 2 times reduced t, 13 times derived, 1 times residual
• residual design of supplementary of 6-(31,9,200) (# 12296)

---

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created: Fri Oct 23 11:12:58 CEST 2009