Constructing defining sets of full designs

Abstract

Defining sets of balanced incomplete block designs (BIBDs) were introduced by Ken Gray. They have been considered for potential applications, not only for their theoretical interest, and various authors have identified minimal defining sets of particular BIBDs or classes of BIBDs, usually among those with small values of λ. In a previous paper, we proved some results on defining sets of full designs, that is, designs comprising one copy each of all the k-tuples on a given set of v elements. We now find defining sets of full designs for general v and k, with 3 ≤ k ≤ v - 3. For k = 3 and for k = 4, we show that these defining sets are minimal.