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New star discrepancy bounds for \((t,m,s)\)-nets and \((t,s)\)-sequences

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Abstract

In this paper, we derive new general upper bounds on the star discrepancy of \((t,m,s)\)-nets and \((t,s)\)-sequences. These kinds of point sets are among the most widely used in quasi-Monte Carlo methods for numerical integration. By our new results, we improve on previous discrepancy bounds and prove a conjecture stated by the second author in an earlier paper.

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Acknowledgments

The authors would like to thank C. Lemieux, F. Pillichshammer and an anonymous referee for comments and suggestions on how to improve this paper.

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Authors and Affiliations

  1. Institut de Mathématiques de Luminy (CNRS), Université d’Aix-Marseille, 163 avenue de Luminy, case 907, 13288 , Marseille cedex 09, France

    Henri Faure

  2. Institut für Finanzmathematik, Universität Linz, Altenbergerstr.69, 4040 , Linz, Austria

    Peter Kritzer

Authors
  1. Henri Faure
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  2. Peter Kritzer
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Corresponding author

Correspondence to Peter Kritzer.

Additional information

Communicated by A. Constantin.

P. Kritzer gratefully acknowledges the support of the Austrian Science Fund (FWF), Project P23389-N18.

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Faure, H., Kritzer, P. New star discrepancy bounds for \((t,m,s)\)-nets and \((t,s)\)-sequences. Monatsh Math 172, 55–75 (2013). https://doi.org/10.1007/s00605-012-0470-1

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  • DOI: https://doi.org/10.1007/s00605-012-0470-1

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