Embeddings of Steiner Quadruple Systems using Extensions of Linear Spaces

Abstract

Using a linear space on \(v\) points with all block sizes \(|B| \equiv 0\) or \(1 \pmod{3}\), Doyen and Wilson construct a Steiner triple system on \(2v+1\) points that embeds a Steiner triple system on \(2|B|+1\) points for each block \(B\). We generalise this result to show that if the linear space on \(v\) points is extendable in a suitable way, there is a Steiner quadruple system on \(2v+2\) points that embeds a Steiner quadruple system on \(2(|B|+1)\) points for each block \(B\).