COMPUTER‐AIDED CONSTRUCTION OF SMALL (M, S)‐OPTIMAL INCOMPLETE BLOCK DESIGNS

Abstract

SummaryA new exchange algorithm for the construction of (M, S)‐optimal incomplete block designs (IBDS) is developed. This exchange algorithm is used to construct 973 (M, S)‐optimal IBDs (v, k, b) for v= 4,…,12 (varieties) with arbitrary v, k (block size) and b (number of blocks). The efficiencies of the “best” (M, S)‐optimal IBDs constructed by this algorithm are compared with the efficiencies of the corresponding nearly balanced incomplete block designs (NBIBDs) of Cheng(1979), Cheng & Wu (1981) and Mitchell & John(1976).