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On the existence of low-diaphony sequences made of digital sequences and lattice point sets

Authors

  • Peter Kritzer,

    Corresponding author
    1. Institut für Finanzmathematik, Universität Linz, Altenbergerstrasse 69, 4040 Linz, Austria. Phone: +43 732 2468 0, Fax: +43 732 2468 4032
    • Institut für Finanzmathematik, Universität Linz, Altenbergerstrasse 69, 4040 Linz, Austria. Phone: +43 732 2468 0, Fax: +43 732 2468 4032
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  • Friedrich Pillichshammer

    1. Institut für Finanzmathematik, Universität Linz, Altenbergerstrasse 69, 4040 Linz, Austria. Phone: +43 732 2468 0, Fax: +43 732 2468 4032
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Abstract

In this paper, we discuss hybrid point sets built from two of the most prominent classes of sequences used in quasi-Monte Carlo methods. We derive an existence result on point sets with low diaphony, where the components of the points involved stem from a digital (t, s)-sequence on the one hand, and from a lattice point set on the other. Moreover, we outline how the hybrid diaphony of the point sets considered in this paper relates to the worst-case integration error in suitable function spaces.

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