Octahedrals in Steiner quadruple systems

Abstract

Any set of 8 blocks of size 4 over an 8-set, isomorphic to {abcd, abxy, acty, adtx, bcyz, bdxz, cdtz, txyz} is called an octahedral configuration which is a generalization of a quadrilateral of Pasch configuration or one half of a minimal 3-(8, 4) trade. In this paper we show that all Hanani's recursive constructions of SQS(v) for v = 2 or 4 (mod 6) contain octahedrads except for v = 4, 10, and 14.