Super-simple Steiner pentagon systems Original Research Article

A Steiner pentagon system of order image image is said to be super-simple if its underlying image-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 image; namely, image and image or image is sufficient, except for image, image and possibly for image. In the process, we also improve an earlier result for the spectrum of super-simple image-BIBDs, removing all the possible exceptions. We also give some new examples of Steiner pentagon packing and covering designs (SPPDs and SPCDs).