Some new 2-resolvable Steiner quadruple systems (Q1321552)

The author proves a general theorem for the construction of 2-resolvable \(S(3,k,v)\) Steiner systems, that is for 3-\((v,k,1)\) designs whose blocks can be partitioned into disjoint 2-\((v,k,1)\) designs. As a consequence he shows that if \(k \equiv 8 \pmod {12}\) and \(k-1\) is a prime power, the existence of a 2-resolvable \(S(3,4,2k)\) implies the existence of a 2- resolvable \(S(3,4,2 (k-1)^ n+2)\) for all \(n\). In particular, 2- resolvable \(S(3,4,2.7^ n+2)\) and 2-resolvable \(S(3,4,2.31^ n+2)\) exist for all \(n\).