The Flower Intersection Problem for Steiner Systems $S(3,4,v),v=4-2^m,5-2^m$

Abstract

We determine those pairs $(k,v)$, $v=4\cdot 2^m,5\cdot 2^m$, for which there exists a pair of Steiner quadruple systems on the same $v$-set, such that the quadruples in one system containing a particular point are the same as those in the other system and moreover the two systems have exactly $k$ other quadruples in common.