Anti-Pasch optimal packings with triples

Abstract

It is shown that for v not equal 6, 7, 10, 11, 12, 13, there exists an optimal packing with triples on v points that contains no Pasch configurations. Furthermore, for all v equivalent to 5 (mod 6), there exists a pairwise balanced design of order v, whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.