t designs with small t, id ge 2000

# 2000: 5-(24,12,11766)

clan: 5-(24,12,11766)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2001: 5-(24,12,11772)

clan: 5-(24,12,11772)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2002: 5-(24,12,11778)

clan: 11-(30,15,906), 3 times derived, 3 times residual
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2003: 5-(25,12,18120)

clan: 11-(30,15,906), 1 times reduced t, 3 times derived, 2 times residual
Tran van Trung construction (left) for 5-(24,12,11778) (# 2002) : der= 5-(24,11,6342) and res= 5-(24,12,11778) - the given design is the residual.

# 2004: 5-(26,13,47565)

clan: 11-(30,15,906), 2 times reduced t, 2 times derived, 2 times residual
Tran van Trung construction with complementary design for 5-(25,12,18120) (# 2003)

# 2005: 5-(26,12,27180)

clan: 11-(30,15,906), 2 times reduced t, 3 times derived, 1 times residual
Tran van Trung construction (left) for 5-(25,12,18120) (# 2003) : der= 5-(25,11,9060) and res= 5-(25,12,18120) - the given design is the residual.

# 2006: 5-(27,13,74745)

clan: 11-(30,15,906), 3 times reduced t, 2 times derived, 1 times residual
Tran van Trung construction (left) for 5-(26,13,47565) (# 2004) : der= 5-(26,12,27180) and res= 5-(26,13,47565) - the given design is the residual.
Tran van Trung construction (right) for 5-(26,12,27180) (# 2005) : der= 5-(26,12,27180) and res= 5-(26,13,47565) - the given design is the derived.

# 2007: 5-(28,14,191015)

clan: 11-(30,15,906), 4 times reduced t, 1 times derived, 1 times residual
Tran van Trung construction with complementary design for 5-(27,13,74745) (# 2006)

# 2008: 5-(24,12,11784)

clan: 5-(24,12,11784)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2009: 5-(24,12,11790)

clan: 5-(24,12,11790)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2010: 5-(24,12,11796)

clan: 5-(24,12,11796)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2011: 5-(24,12,11802)

clan: 5-(24,12,11802)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2012: 5-(24,12,11808)

clan: 5-(24,12,11808)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2013: 5-(24,12,11814)

clan: 5-(24,12,11814)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2014: 5-(24,12,11820)

clan: 5-(24,12,11820)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2015: 5-(24,12,11826)

clan: 5-(24,12,11826)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2016: 5-(24,12,11832)

clan: 5-(24,12,11832)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2017: 5-(24,12,11838)

clan: 5-(24,12,11838)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2018: 5-(24,12,11844)

clan: 5-(24,12,11844)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2019: 5-(24,12,11850)

clan: 5-(24,12,11850)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2020: 5-(24,12,11856)

clan: 15-(32,16,4), 2 times reduced t, 4 times derived, 4 times residual
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2021: 5-(24,12,11862)

clan: 5-(24,12,11862)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2022: 5-(24,12,11868)

clan: 5-(24,12,11868)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2023: 5-(24,12,11874)

clan: 5-(24,12,11874)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2024: 5-(24,12,1188)

clan: 5-(24,12,1188)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2025: 5-(24,12,11880)

clan: 5-(24,12,11880)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2026: 5-(24,12,11886)

clan: 5-(24,12,11886)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2027: 5-(24,12,11892)

clan: 5-(24,12,11892)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2028: 5-(24,12,11898)

clan: 5-(24,12,11898)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2029: 5-(24,12,11904)

clan: 5-(24,12,11904)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2030: 5-(24,12,11910)

clan: 5-(24,12,11910)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2031: 5-(24,12,11916)

clan: 5-(24,12,11916)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2032: 5-(24,12,11922)

clan: 5-(24,12,11922)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2033: 5-(24,12,11928)

clan: 5-(24,12,11928)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2034: 5-(24,12,11934)

clan: 11-(30,15,918), 3 times derived, 3 times residual
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2035: 5-(24,12,11940)

clan: 5-(24,12,11940)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2036: 5-(24,12,11946)

clan: 5-(24,12,11946)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2037: 5-(24,12,11952)

clan: 5-(24,12,11952)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2038: 5-(24,12,11958)

clan: 5-(24,12,11958)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2039: 5-(24,12,11964)

clan: 5-(24,12,11964)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2040: 5-(24,12,11970)

clan: 7-(24,12,1470), 2 times reduced t
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23
Tran van Trung construction with complementary design for 5-(23,11,4410) (# 9003)
design 6-(24,12,4410) (# 9005) with respect to smaller t
Tran van Trung construction (left) for 5-(23,12,7560) (# 9010) : der= 5-(23,11,4410) and res= 5-(23,12,7560) - the given design is the residual.
supplementary design of 6-(24,12,14154) (# 9014) with respect to smaller t

# 2041: 5-(24,12,11976)

clan: 5-(24,12,11976)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2042: 5-(24,12,11982)

clan: 5-(24,12,11982)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2043: 5-(24,12,11988)

clan: 5-(24,12,11988)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2044: 5-(24,12,11994)

clan: 5-(24,12,11994)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2045: 5-(24,12,12000)

clan: 5-(24,12,12000)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2046: 5-(24,12,12006)

clan: 5-(24,12,12006)
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2047: 5-(24,12,12012)

clan: 13-(32,16,231), 4 times derived, 4 times residual
$ PSL(2,23) $ % -group 3 PSL 2 23 PSL_2_23

# 2048: 5-(25,12,18480)

clan: 13-(32,16,231), 1 times reduced t, 4 times derived, 3 times residual
Tran van Trung construction (left) for 5-(24,12,12012) (# 2047) : der= 5-(24,11,6468) and res= 5-(24,12,12012) - the given design is the residual.

# 2049: 5-(26,13,48510)

clan: 13-(32,16,231), 2 times reduced t, 3 times derived, 3 times residual
Tran van Trung construction with complementary design for 5-(25,12,18480) (# 2048)

# 2050: 5-(26,12,27720)

clan: 13-(32,16,231), 2 times reduced t, 4 times derived, 2 times residual
Tran van Trung construction (left) for 5-(25,12,18480) (# 2048) : der= 5-(25,11,9240) and res= 5-(25,12,18480) - the given design is the residual.

# 2051: 5-(27,13,76230)

clan: 13-(32,16,231), 3 times reduced t, 3 times derived, 2 times residual
Tran van Trung construction (left) for 5-(26,13,48510) (# 2049) : der= 5-(26,12,27720) and res= 5-(26,13,48510) - the given design is the residual.
Tran van Trung construction (right) for 5-(26,12,27720) (# 2050) : der= 5-(26,12,27720) and res= 5-(26,13,48510) - the given design is the derived.

# 2052: 5-(28,14,194810)