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On the Star Discrepancy of Digital Nets and Sequences in Three Dimensions

In: Monte Carlo and Quasi-Monte Carlo Methods 2004

Author

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  • Peter Kritzer

    (University of Salzburg, Department of Mathematics)

Abstract

Summary By relating the star discrepancy of a digital (t, m, 3)-net to that of a digital (t, 2)-sequence, we obtain new upper bounds on the star discrepancy of digital (t, m, 3)-nets. From these results, we derive new upper bounds on the star discrepancy of digital (t, 3)-sequences. We also show the existence of (0, m, 4)-nets with particularly low star discrepancy.

Suggested Citation

  • Peter Kritzer, 2006. "On the Star Discrepancy of Digital Nets and Sequences in Three Dimensions," Springer Books, in: Harald Niederreiter & Denis Talay (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2004, pages 273-287, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-31186-7_17
    DOI: 10.1007/3-540-31186-6_17
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