On group divisible covering designs Original Research Article

A group divisible covering design (GDCD) with block size k and group-type gu is defined to be a triple (X, G, B) where X is a gu-set (of points), G is a partition of X into g-subsets (called groups), B is a set of k-subsets of X (called blocks) such that a group and a block contain at most one common point and every pair of points from distinct groups occurs in at least one block. The covering number, C(k,gu), is the number of blocks in a minimum GDCD with block size k and group-type gu. The values of the function C(3,gu) are determined in this paper for all positive integers g and u⩾3.