Construction techniques for anti-Pasch Steiner triple systems

Four methods for constructing anti-Pasch Steiner triple systems are develop ed. The first generalises a construction of Stinson and Wei to obtain a gen eral singular direct product construction. The second generalises the Bose construction. The third employs a construction due to Lu. The fourth employ s 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 = 1 or 7 (mod 18), for v = 49 (mod 72) , and for many other values of v.