Optimal Incomplete Block Designs

A classical problem in experimental design is the construction of incomplete block designs, i.e., designs that group r replications of each of v treatments into b blocks of size k. This report presents optimal incomplete block designs which were constructed utilizing the connection between the concurrence matrix of a design and a regular graph. The class of regular graph (RG) designs, conjectured to be optimal, is defined. The results of a systematic search of the class of RG designs are given for all cases in which v is less than or equal to 12 and r is less than or equal to 10. In nearly every case, the optimum design with respect to each of the three criteria, D-optimality, A-optimality (identical with) = efficiency and E-optimality, is determined. Many of these designs are new and are tabulated in this report. 2 tables.