Steiner quadruple systems having a prescribed number of quadruples in common (Q1071773)

The intersection problem for a parameter set t,v,k,\(\lambda\) is to determine the set of values i, such that there exist two t- (v,k,\(\lambda)\) designs with precisely i blocks in common. This paper solves the intersection problem for 3-(v,4,1) designs with \(v=2^ n\), \(5\cdot 2^ n\), \(7\cdot 2^ n\), \(n>1\). The general problem for 3- (v,4,1) designs remains open. The method used is a well-known variant on the doubling construction for Steiner quadruple systems.