On Some Combinatorial Structures Constructed from the Groups 𝐿(3,5), 𝑈(5,2), and 𝑆(6,2)

Table 4

Structures constructed from 𝐿(3,5), 𝑈(5,2), and 𝑆(6,2).

Combinatorial structure	The full automorphism group
2−(31,6,1) design	𝐿(3,5)
2−(31,6,100) design	𝐿(3,5)
2−(31,10,300) design	𝐿(3,5)
2−(31,15,700) design	𝐿(3,5)
2−(31,3,25) design	𝐿(3,5)
2−(31,12,550) design	𝐿(3,5)
2−(31,15,875) design	𝐿(3,5)
2−(28,12,11) design	𝑆(6,2)
2−(28,4,5) design	𝑆(6,2)
2−(28,10,40) design	𝑆(6,2)
2−(36,16,12) design	𝑆(6,2)
2−(36,8,6) design	𝑆(6,2)
2−(36,12,33) design	𝑆(6,2)
2−(36,6,8) design	𝑆(6,2)
2−(63,31,15) design	PGL(6,2)
2−(28,4,4) design	𝑈(3,3)∶𝑍2
2−(28,4,1) design	𝑈(3,3)∶𝑍2
SRG(63,30,13,15)	𝑆(6,2)
SRG(120,56,28,24)	𝑂^+8(2)∶𝑍2
SRG(135,64,28,32)	𝑂^+8(2)∶𝑍2
SRG(165,36,3,9)	𝑈(5,2)∶𝑍2
SRG(176,40,12,8)	𝑈(5,2)∶𝑍2
SRG(297,40,7,5)	𝑈(5,2)∶𝑍2
SRG(1408,567,246,216)	𝐹𝑖21∶𝑍2