Linear Programming Bounds for Ordered Orthogonal Arrays and (T, M, S)-nets

  • William J. Martin
Conference paper


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • William J. Martin
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of WinnipegWinnipegCanada

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