A Census of Highly Symmetric Steiner Designs

Abstract

In this chapter, we present the complete determination of all flag-transitive Steiner t-designs with t ≥ 3. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs, without attempting to be encyclopedic. For a detailed description of the respective designs with their groups of automorphisms and for further surveys concerning in particular highly symmetric Steiner 2-designs, we refer to Chapter 4 as well as to [22, Sect. 1, 2], [43, Chap. 2.3, 2.4, 4.4], [79], [81], and [125].