On the automorphisms of designs constructed from finite simple groups

Here we study the automorphism groups of 1-designs constructed from finite nonabelian simple groups by using two methods presented in Moori (Information Security, Coding Theory and Related Combinatorics, 2011) [9]. We obtain some general results for both and improve one of these methods. In an application to the sporadic Mathieu groups Mn, we are able to retrieve the Steiner systems S(t, t+ 3, n) where (n, t) ∈ {(22, 3), (23, 4), (24, 5)}.