Linear Programming Bounds for Ordered Orthogonal Arrays and (T, M, S)-nets
A recent theorem of Schmid and Lawrence establishes an equivalence between (T, M, S)-nets and ordered orthogonal arrays. This leads naturally to a search both for constructions and for bounds on the size of an ordered orthogonal array. Subsequently, Martin and Stinson used the theory of association schemes to derive such a bound via linear programming. In practice, this involves large-scale computation and issues of numerical accuracy immediately arise. We propose a hybrid technique which gives lower bounds — obtained in exact arithmetic — on the number of rows in an ordered orthogonal array. The main result of the paper is a table showing the implications of these bounds for the study of (T, M, S)-nets.
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