The fundamental construction for 3-designs
The purpose of this paper is to extend the fundamental construction for group divisible designs of Wilson to one suitable for use in the construction of 3-designs. An important part of this is the generalization of the concept of a group divisible design and this is discussed in some detail. The construction simplifies in some special cases to similar known constructions. The construction is used to present simplified proofs of known results, especially for Steiner quadruple systems, that is 3-designs with four points in every block, and to give recursive theorems both for the construction of Steiner quadruple systems and for the construction of more general 3-designs with multiple block sizes.
scientific article; zbMATH DE number 500612
scientific article