$101$ Anti-Pasch Steiner Triple Systems of Order $19$

Abstract

An algorithm to construct anti-Pasch Steiner triple systems is described and utilized to construct $101$ such systems of order $19$. It is also proved that no anti-Pasch $STS(19)$ contains a non-trivial subsystem. Furthermore, anti-Pasch $STS(19)$s with prescribed automorphisms are identified.