Boolean 2-designs and the embedding of a 2-design in a group

Abstract

We try to embed a t-design in a finite commutative group in such a way that the sum of the k points of a block is zero. We can compute the number of blocks of the boolean 2-design having all the non zero vectors of $(Z_2{)}^n$ as the set of points and the k-subsets of elements the sum of which is zero as blocks.

Extended abstract of a talk given at the conference Combinatorics 2008, Costermano (Italy) 22-28 June 2008. Removed Corollary 9 (false!)