Super‐simple holey Steiner pentagon systems and related designs

A Steiner pentagon system of order v (SPS(v)) is said to be super‐simple if its underlying (v, 5, 2)‐BIBD is super‐simple; that is, any two blocks of the BIBD intersect in at most two points. It is well known that the existence of a holey Steiner pentagon system (HSPS) of type T implies the existence of a (5, 2)‐GDD of type T. We shall call an HSPS of type T super‐simple if its underlying (5, 2)‐GDD of type T is super‐simple; that is, any two blocks of the GDD intersect in at most two points. The existence of HSPSs of uniform type hn has previously been investigated by the authors and others. In this article, we focus our attention on the existence of super‐simple HSPSs of uniform type hn.