Construction techniques for anti-Pasch Steiner triple systems

Ling, A. C. H.; Colbourn, C. J.; Grannell, M. J. and Griggs, T. S. (2000). Construction techniques for anti-Pasch Steiner triple systems. Journal of the London Mathematical Society, 61(3) p. 641.

URL: http://dx.doi.org/10.1112/S0024610700008838

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 two. As a consequence of these constructions we are able to produce anti-Pasch systems of order $v$ for $v\equiv 1$ or $7$ (mod 18), for $v\equiv 49$ (mod 72), and for many other values of $v$ .