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.

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