Anti-Pasch optimal packings with triples

Demirkale, Fatih; Donovan, Diane and Grannell, Mike (2019). Anti-Pasch optimal packings with triples. Journal of Combinatorial Designs, 27(6) pp. 353–368.

DOI: https://doi.org/10.1002/jcd.21646

Abstract

It is shown that for v ≠ 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 ≡ 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.

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