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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© 2000 Springer-Verlag Berlin Heidelberg
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Martin, W.J. (2000). Linear Programming Bounds for Ordered Orthogonal Arrays and (T, M, S)-nets. In: Niederreiter, H., Spanier, J. (eds) Monte-Carlo and Quasi-Monte Carlo Methods 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59657-5_25
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DOI: https://doi.org/10.1007/978-3-642-59657-5_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66176-4
Online ISBN: 978-3-642-59657-5
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