Construction Procedures for t-designs and the Existence of New Simple 6–designs

We describe procedures for finding t-designs with prescribed automorphism groups and apply these methods to finding t-designs on 20 points with either PGL2(19) or PSL2(19) as an automorphism group. We produce two non-isomorphic simple 6-designs with parameters 6-(20,9,112) and automorphism group PSL2(19). It has been previously shown that if q < 19, simple 6-designs on v = q + 1 points do not exist with automorphism group PSL2(q). Hence v = 20 is the smallest v = q +1 where simple 6-designs occur with automorphism group PSL2(q).

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