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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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Volume 16, Issue 3-4


A good permutation for one-dimensional diaphony

Florian Pausinger / Wolfgang Ch. Schmid
Published Online: 2010-11-05 | DOI: https://doi.org/10.1515/mcma.2010.015


In this article we focus on two aspects of one-dimensional diaphony of generalised van der Corput sequences in arbitrary bases. First we give a permutation with the best distribution behaviour concerning the diaphony known so far. We improve a result of Chaix and Faure from 1993 from a value of 1.31574 . . . for a permutation in base 19 to 1.13794 . . . for our permutation in base 57. Moreover for an infinite sequence X and its symmetric version , we analyse the connection between the diaphony F(X, N) and the L 2-discrepancy using another result of Chaix and Faure. Therefore we state an idea how to get a lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b.

Keywords.: Diaphony; generalised van der Corput sequence

About the article

Received: 2009-12-01

Revised: 2010-09-22

Published Online: 2010-11-05

Published in Print: 2010-12-01

Citation Information: Monte Carlo Methods and Applications, Volume 16, Issue 3-4, Pages 307–322, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma.2010.015.

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