Combinatorial constructions for optimal supersaturated designs

Abstract

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( f NOD) criterion is used as a measure of non-orthogonality of U-type designs, and a lower bound of E( f NOD) which can serve as a benchmark of design optimality is obtained. A U-type design is E( f NOD)-optimal if its E( f NOD) value achieves the lower bound. In most cases, E( f NOD)-optimal U-type designs are supersaturated. We show that a kind of E( f NOD)-optimal designs are equivalent to uniformly resolvable designs. Based on this equivalence, several new infinite classes for the existence of E( f NOD)-optimal designs are then obtained.