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. E(fNOD) criterion is used as a measure of non-orthogonality of U-type designs, and a lower bound of E(fNOD) which can serve as a benchmark of design optimality is obtained. A U-type design is E(fNOD)-optimal if its E(fNOD) value achieves the lower bound. In most cases, E(fNOD)-optimal U-type designs are supersaturated. We show that a kind of E(fNOD)-optimal designs are equivalent to uniformly resolvable designs. Based on this equivalence, several new in<nite classes for the existence of E(fNOD)-optimal designs are then obtained. c © 2003 Elsevier B.V. All rights reserved.