Improvements on Low Discrepancy One-Dimensional Sequences and Two-Dimensional Point Sets

Henri Faure ()
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Henri Faure: UMR 6206 CNRS, Institut de Mathématiques de Luminy

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 327-341 from Springer

Abstract: Summary We obtain significant improvements for the star discrepancy D* of generalized van der Corput sequences by means of linear digit scramblings (see Section 5.2 for the definition). We also find a new lower bound for the extreme discrepancy D of these sequences which permits to show that linearly-scrambled sequences are set in a good place among generalized van der Corput sequences. Finally, we derive the corresponding properties for generalized Hammersley point sets in arbitrary bases and link recent developments in base 2 by Kritzer, Larcher and Pillichshammer to former studies of Béjian and the author.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_19

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DOI: 10.1007/978-3-540-74496-2_19

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