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

  • William J. Martin
Conference paper

Abstract

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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References

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    A. T. Clayman, K. M. Lawrence, G. L. Mullen, H. Niederreiter and N. J. A. Sloane. Updated tables of parameters of (T, M, S)-nets. To appear inJournal of Combinatorial Designs.Google Scholar
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    . K. M. Lawrence. A combinatorial interpretation of(t, m, s)-nets in baseb. Journal of Combinatorial Designs 4(1996), 275 – 293.CrossRefzbMATHMathSciNetGoogle Scholar
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    W. J. Martin and D. R. Stinson. A generalized Rao bound for ordered orthogonal arrays and (t, m, s)-nets.Canadian Math. Bull. to appear.Google Scholar
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    W. J. Martin and D. R. Stinson. Association schemes for ordered orthogonal arrays and (t, m, s)-nets.Canadian J. Math., to appear.Google Scholar
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    W. Ch. Schmid.(t, m, s)-nets: Digital constructions and combinatorial aspects. Doctoral Dissertation, University of Salzburg, (1995).Google Scholar

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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