Quasipolynomial-time canonical form for steiner designs

A Steiner 2-design is a finite geometry consisting of a set of "points" together with a set of "lines" (subsets of points of uniform cardinality) such that each pair of points belongs to exactly one line. In this paper we analyse the individualization/refinement heuristic and conclude that after individualizing O(log n) points (assigning individual colors to them), the refinement process gives each point an individual color. The following consequences are immediate: (a) isomorphism of Steiner 2-designs can be tested in nO(log n) time, where n is the number of lines; (b) a canonical form of Steiner 2-designs can be computed within the same time bound; (c) all isomorphisms between two Steiner 2-designs can be listed within the same time bound; (d) the number of automorphisms of a Steiner 2-design is at most nO(log n) (a fact of interest to finite geometry and group theory.)