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Dispersion of digital (0, m, 2)-nets

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Abstract

We study the dispersion of digital (0, m, 2)-nets; i.e. the size of the largest axes-parallel box within such point sets. Digital nets are an important class of low-discrepancy point sets. We prove tight lower and upper bounds for certain subclasses of digital nets where the generating matrices are of triangular form and compute the dispersion of special nets such as the Hammersley point set exactly.

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Authors and Affiliations

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

    Ralph Kritzinger

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  1. Ralph Kritzinger
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Correspondence to Ralph Kritzinger.

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Communicated by Adrian Constantin.

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The author is supported by the Austrian Science Fund (FWF), Project F5509-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”

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Kritzinger, R. Dispersion of digital (0, m, 2)-nets. Monatsh Math 195, 155–171 (2021). https://doi.org/10.1007/s00605-021-01525-9

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  • DOI: https://doi.org/10.1007/s00605-021-01525-9

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