Construction Techniques for Anti-Pasch Steiner Triple Systems

Abstract

Four methods for constructing anti-Pasch Steiner triple systems are developed. The first generalises a construction of Stinson and Wei to obtain a general singular direct product construction. The second generalises the Bose construction. The third employs a construction due to Lu. The fourth employs Wilson-type inflation techniques using Latin squares having no subsquares of order 2. As a consequence of these constructions we are able to produce anti-Pasch systems of order v for v 31 or 7 (mod 18), for v ≡ 49 (mod 72), and for many other values of v.