Small group divisible Steiner quadruple systems

A group divisible Steiner quadruple system, is a triple (X, H, B) where X is a v-element set of points, H = {H1, H2,... ,H r] is a partition of X into holes and B is a collection of 4-element subsets of X called blocks such that every 3-element subset is either in a block or a hole but not both. In this article we investigate the existence and non-existence of these designs. We settle all parameter situations on at most 24 points, with 6 exceptions. A uniform group divisible Steiner quadruple system is a system in which all the holes have equal size. These were called by Mills G-designs and their existence is completely settled in this article