3-designs from PSL(2, q) with q = 1(mod 4)

Abstract

In this paper, we consider the action of the group PSL(2, q) on the finite projective line GF(q) U {∞} when q is a prime power congruent to 1 modulo 4 and construct several simple 3-(q+1, 5, λ) designs admitting PSL(2, q) as an automorphism group. Most of these designs with the given parameter sets were previously unknown.