Intersection problem of Steiner systems S(3,4,2v) (Q1097890)

This paper gives an almost complete solution to the intersection problem for Steiner quadruple systems of orders \(v\equiv 4\) or 8 (mod 12). The intersection problem remains open for systems of orders \(v\equiv 2\) or 10 (mod 12). The two main results are: If a complete solution for the cases \(v\in \{16,20,28\}\) is found then this implies a complete solution for all \(v\equiv 4\) or 8 (mod 12). For \(v\equiv 4\) or 8 (mod 12), the intersection problem is solved with three possible exceptions for each value of v. The techniques used are recursive, and rely heavily on embedding techniques for Steiner quadruple systems.