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Monte-Carlo and Quasi-Monte Carlo Methods 1998 pp 436–447Cite as

Improvements and Extensions of the “Salzburg Tables” by Using Irreducible Polynomials

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Abstract

The quality of quasi-Monte Carlo methods mainly depends on the distribution properties of the underlying (deterministic) point set. The theory of digital nets provides a method for the construction of extremely well distributed point sets in thes-dimensional unit cube.

This article is an extension of the work in [LLNS96] where a special class of these point sets was introduced. We present improved existence results for digital nets over finite fields \({\mathbb{F}_q}\)of arbitrary prime-power orderq, and show great improvements for concrete constructions in the binary case.

Research supported by the projects P12441-MAT (FWF) and 6788 (OeNB)

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, A-5020, Salzburg, Austria

    Wolfgang Ch. Schmid

Authors
  1. Wolfgang Ch. Schmid
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Editor information

Editors and Affiliations

  1. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, 1010, Vienna, Austria

    Harald Niederreiter

  2. Claremont Graduate University, 925 N. Dartmouth Avenue, 91711, Claremont, CA, USA

    Jerome Spanier

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© 2000 Springer-Verlag Berlin Heidelberg

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Schmid, W.C. (2000). Improvements and Extensions of the “Salzburg Tables” by Using Irreducible Polynomials. In: Niederreiter, H., Spanier, J. (eds) Monte-Carlo and Quasi-Monte Carlo Methods 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59657-5_30

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  • DOI: https://doi.org/10.1007/978-3-642-59657-5_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66176-4

  • Online ISBN: 978-3-642-59657-5

  • eBook Packages: Springer Book Archive

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