Concerning cyclic group divisible designs with block size three

Resolvable Modified Group Divisible Designs with Block Size Three

A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. # 2005 Wiley Periodicals, Inc. J Combin Designs 15: 2–14, 2007

A class of group divisible designs with block size three and index λ

We investigate the existence of group divisible designs (GDDs) with block size three, group-type gw and index λ. We prove that the elementary necessary conditions for the existence of such a GDD are also sufficient, which generalizes the result of Colbourn, Hoffman and Rees.

A Family of Group Divisible Designs of Block Size Four and Three Groups With l1=2 and l2=1 Using MOLS

We give a construction for a new family of Group Divisible Designs (6s+ 2, 3, 4; 1, 2) using Mutually Orthogonal Latin Squares for all positive integers s. Consequently, we have proved that the necessary conditions are sufficient for the existence of GDD’s of block size four with three groups, λ1=2 and λ2=1.

Resolvable holey group divisible designs with block size three

Modified group divisible designs with block size four

The existence of modiied group divisible designs with block size four is settled with a handful of possible exceptions.