A good permutation for one-dimensional diaphony

Pausinger Florian () and Schmid Wolfgang Ch. ()
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Pausinger Florian: Fachbereich Mathematik, Universität Salzburg, Hellbrunner Straße 34, A-5020 Salzburg, Austria. E-mail:
Schmid Wolfgang Ch.: Fachbereich Mathematik, Universität Salzburg, Hellbrunner Straße 34, A-5020 Salzburg, Austria. E-mail:

Monte Carlo Methods and Applications, 2010, vol. 16, issue 3-4, 307-322

Abstract: 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 L2-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 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1515/mcma.2010.015

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