Constructing block designs with a prescribed automorphism group using genetic algorithm

Abstract

We propose a method of constructing block designs which combine genetic algorithm and a method for constructing designs with a prescribed automorphism group using tactical decompositions (i.e., orbit matrices). We apply this method to construct new Steiner systems with parameters S(2,5,45) $S(2,5,45)$ and new symmetric designs with parameters (71, 15, 3).