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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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1569-3961
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Volume 12, Issue 1

Issues

A best possible upper bound on the star discrepancy of (t, m, 2)-nets

Josef Dick
  • The first author is supported by the Australian Research Council under its Center of Excellence Program.
  • School of Mathematics, University of New South Wales, Sydney 2052, Australia.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Peter Kritzer
  • The second author is supported by the Austrian Research Foundation (FWF), Projects P17022-N12 and S8311-MAT.
  • Corresponding Author, Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar

We study the star discrepancy of (t, m, 2)-nets and (t, 2)-sequences in arbitrary base b. We give best possible upper bounds on the star discrepancy of (t, m, 2)-nets and show new upper bounds on the star discrepancy of (t, 2)-sequences. By these results, which shall be obtained by combinatorial arguments, we improve existing upper bounds on the star discrepancy of such point sets.

Key Words: (t, m, s)-net,; (t, s)-sequence,; star discrepancy

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Published Online:

Published in Print: 2006-03-01


Citation Information: Monte Carlo Methods and Applications mcma, Volume 12, Issue 1, Pages 1–17, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/156939606776886643.

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Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Peter Kritzer
Journal of Complexity, 2006, Volume 22, Number 3, Page 336
[2]
Henri Faure and Peter Kritzer
Monatshefte für Mathematik, 2013, Volume 172, Number 1, Page 55
[3]
Johann S. Brauchart and Josef Dick
Numerische Mathematik, 2012, Volume 121, Number 3, Page 473

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