Homogeneous and ultrahomogeneous Steiner systems

A Steiner system (or t - (v, k, 1) design) S is said to be homogeneous if, whenever the substructures induced on two finite subsets S, and S-2 of S are isomorphic, there is at least one automorphism of S mapping S-1 onto S-2, and is said to be ultrahomogeneous if each isomorphism between the substructures induced on two finite subsets of S can be extended to an automorphism of S. We give a complete classification of all homogeneous and ultrahomogeneous Steiner systems. (C) 2003 Wiley Periodicals, Inc.