Holey Steiner pentagon systems and related designs

Abstract

Certain types of holey Steiner pentagon systems (HSPSs) are investigated. New HSPSs are found, which improve an earlier existence result. These HSPSs are used to solve the existence of Steiner pentagon packing designs (SPPDs). It is proved that an SPPD always exists with a handful of possible exceptions, in which the largest unknown order is 189. From these HSPSs, new results are also found for holey perfect Mendelsohn designs and Steiner pentagon covering designs.