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On Hybrid Point Sets Stemming from Halton-Type Hammersley Point Sets and Polynomial Lattice Point Sets

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Monte Carlo and Quasi-Monte Carlo Methods (MCQMC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 324))

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Abstract

In this paper we consider finite hybrid point sets that are the digital analogs to finite hybrid point sets introduced by Kritzer. Kritzer considered hybrid point sets that are a combination of lattice point sets and Hammersley point sets constructed using the ring of integers and the field of rational numbers. In this paper we consider finite hybrid point sets whose components stem from Halton-type Hammersley point sets and lattice point sets which are constructed using the arithmetic of the ring of polynomials and the field of rational functions over a finite field. We present existence results for such finite hybrid point sets with low discrepancy.

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Acknowledgements

The author is supported by the Austrian Science Fund (FWF): Project F5505-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”. Furthermore, the author appreciates several valuable comments by the anonymous referees.

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Authors and Affiliations

  1. Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz, Altenbergerstr.69, 4040, Linz, Austria

    Roswitha Hofer

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  1. Roswitha Hofer
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Correspondence to Roswitha Hofer .

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Editors and Affiliations

  1. INRIA Rennes Bretagne-Atlantique, Campus Universtaire de Beaulieu, Rennes, France

    Bruno Tuffin

  2. Département d’informatique et de Recherche Opérationnelle (DIRO), Université de Montréal, Montreal, QC, Canada

    Pierre L'Ecuyer

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Hofer, R. (2020). On Hybrid Point Sets Stemming from Halton-Type Hammersley Point Sets and Polynomial Lattice Point Sets. In: Tuffin, B., L'Ecuyer, P. (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2018. Springer Proceedings in Mathematics & Statistics, vol 324. Springer, Cham. https://doi.org/10.1007/978-3-030-43465-6_12

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