Combinatorial constructions for optimal supersaturated designs

Combinatorial designs have long had substantial application in the statistical design of experiments, and in the theory of error-correcting codes. Applications in experimental and theoretical computer science, communications, cryptography and networking have also emerged in recent years. In this paper, we focus on a new application of combinatorial design theory in experimental design theory. <f>E(fNOD)</f> criterion is used as a measure of non-orthogonality of U-type designs, and a lower bound of <f>E(fNOD)</f> which can serve as a benchmark of design optimality is obtained. A U-type design is <f>E(fNOD)</f>-optimal if its <f>E(fNOD)</f> value achieves the lower bound. In most cases, <f>E(fNOD)</f>-optimal U-type designs are supersaturated. We show that a kind of <f>E(fNOD)</f>-optimal designs are equivalent to uniformly resolvable designs. Based on this equivalence, several new infinite classes for the existence of <f>E(fNOD)</f>-optimal designs are then obtained. [Copyright &y& Elsevier]