Group divisible designs with two associate grasses: n=2 or m=2

Abstract

In this paper ive iind necessary and sufficient conditions For the existence of a group divisible design GDD(n, m) of index (lambda(1), lambda(2)) in which n = 2 or m = 2, thereby completing the solution of the existence problem for all n, m, lambda(1), and lambda(2). In the process. necessary and sufficient conditions are found For the existence of an x-regular partial triple system whose complement in lambda K-n has a 1-factorization. (C) 1998 Academic Press.