Kirkman covering designs with even-sized holes

A Kirkman holey covering design, denoted by KHCD ( g u ) , is a resolvable group-divisible covering design of type g u . Each of its parallel class contains one block of size δ , while other blocks have size 3. Here δ is equal to 2, 3 and 4 when g u ≡ 2 , 3 and 4 (mod 3) in turn. In this paper, we study the existence problem of a KHCD ( g u ) which has minimum possible number of parallel classes, and give a solution for most values of even g and u .