Some new 3-designs invariant under the groups Sz(8) and S6(2)

Abstract

In this paper, we determine all simple block-transitive 3-designs on 65 points with block stabilizer of order greater than 2, admitting the 2-transitive action of the group [Formula: see text]. As a result, we find 23 3-designs on 65 points that have [Formula: see text] as an automorphism group. Also we construct four 3-([Formula: see text]) designs for [Formula: see text] and two 3-([Formula: see text]) designs for [Formula: see text]. All of these designs have [Formula: see text] as the full automorphism group. Some of these designs are flag and anti-flag-transitive.