Intersections of Steiner systems S(3,4,v) with \(v=5\cdot 2^ n\) (Q1063869)

In the paper the block intersection problem for Steiner quadruple systems (SQS) having orders \(v=5\cdot 2^ n\), \(n\geq 2\) is examined. The main result is \(I_ v-\{q_ v-17\}\subset J(v),\) for all \(v=5\cdot 2^ n\), \(n\geq 2\), where \(q_ v=v\cdot (v-1)\cdot (v-2)/24\), \(I_ v=\{0,1,2,...,q_ v-I4,q_ v-I2,q_ v-8,q_ v\}\) for \(v\geq 8\), and \(J(v)=\{k:\exists SQS(v),(Q,q_ 1),(Q,q_ 2)\) such that \(| q_ 1\cap q_ 2| =k\}\).