Resolvable generalized difference matrices: Existence and applications

Difference matrices, elsewhere also called difference schemes, form a useful tool in the construction of various interesting combinatorial objects such as orthogonal arrays. In this paper, we introduce the concept of a resolvable generalized difference matrix (RGDM) of strength t. The task of the paper is to study the existence and applications of RGDMs. As a result, many new classes of RGDMs are presented. In addition, some approaches of constructing 2-compatible CDPs by using RGDMs of strength three are established. With those constructions, we are able to make a big improvement on the known existence of orbit-disjoint CDPs.