Super-simple Steiner pentagon systems

A Steiner pentagon system of order vv(SPS(v))(SPS(v)) is said to be super-simple if its underlying (v,5,2)(v,5,2)-BIBD is super-simple; that is, any two blocks of the BIBD intersect in at most two points. In this paper, it is shown that the necessary condition for the existence of a super-simple SPS(v)SPS(v); namely, v⩾5v⩾5 and v≡1v≡1 or 5(mod10) is sufficient, except for v=5v=5, 1515 and possibly for v=25v=25. In the process, we also improve an earlier result for the spectrum of super-simple (v,5,2)(v,5,2)-BIBDs, removing all the possible exceptions. We also give some new examples of Steiner pentagon packing and covering designs (SPPDs and SPCDs).