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A good permutation for one-dimensional diaphony

Author

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  • Pausinger Florian

    (Fachbereich Mathematik, Universität Salzburg, Hellbrunner Straße 34, A-5020 Salzburg, Austria. E-mail:)

  • Schmid Wolfgang Ch.

    (Fachbereich Mathematik, Universität Salzburg, Hellbrunner Straße 34, A-5020 Salzburg, Austria. E-mail:)

Abstract

In this article we focus on two aspects of one-dimensional diaphony of generalised van der Corput sequences in arbitrary bases. First we give a permutation with the best distribution behaviour concerning the diaphony known so far. We improve a result of Chaix and Faure from 1993 from a value of 1.31574 . . . for a permutation in base 19 to 1.13794 . . . for our permutation in base 57. Moreover for an infinite sequence X and its symmetric version , we analyse the connection between the diaphony F(X, N) and the L 2-discrepancy using another result of Chaix and Faure. Therefore we state an idea how to get a lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b.

Suggested Citation

  • Pausinger Florian & Schmid Wolfgang Ch., 2010. "A good permutation for one-dimensional diaphony," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 307-322, January.
    • Handle: RePEc:bpj:mcmeap:v:16:y:2010:i:3-4:p:307-322:n:8
    DOI: 10.1515/mcma.2010.015
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