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

Peter Kritzer ()
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Peter Kritzer: University of Salzburg, Department of Mathematics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 273-287 from Springer

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.

Keywords: Prime Power; Linear Independence; Star Discrepancy; Neutral Element; Weighted Sobolev Space (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_17

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DOI: 10.1007/3-540-31186-6_17

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