Simple Steiner Quadruple Systems

A block design is sometimes said to be simple if it contains no nontrivial subsystems. Doyen [2] showed that there exists a simple triple system for all possible orders v = 1 or 3 (mod 6). In this paper we consider the analogous problems for Steiner quadruple systems. In particular, several recursive constructions for simple quadruple systems are given thereby establishing that the spectrum for these systems is infinite.