Resolvable group divisible designs have been instrumental in the construction of other types of combinatorial designs. The necessary conditions for the existence of a resolvable group divisible design with block size k have been proved to be sufficient for the case when k=3. However, the case for k=4 has remained open for a long time. Many researchers have been involved in investigating the existence of resolvable group divisible designs.

The main contribution of the paper is that it improves the known results for the existence of resolvable group divisible designs and gives an almost complete solution to a new main class.

Wilson’s construction on group divisible designs is the fundamental one in the construction of various types of combinatorial designs. Group divisible designs act as the "master designs" in the construction method. Hence, the existence of group divisible designs is crucial to that of other types of designs. Resolvable group divisible designs are a special class of group divisible designs whose blocks can be partitioned into parallel classes each of which partitions the point set of the design. Resolvable group divisible designs are useful in the constructions of both group divisible designs and other types of combinatorial designs.

My supervisor, Professor Zhu Lie of the Department of Mathematics at Suzhou University, had originally posed the resolvable group divisible designs problem to me as a possible thesis topic in 1994. Although I wasn’t able to make any headway at that time, the problem continued to gnaw at me in the ensuing years and I eventually was able to make some progress.