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Vandermonde Nets and Vandermonde Sequences

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 163)

Abstract

A new family of digital nets called Vandermonde nets was recently introduced by the authors. We generalize the construction of Vandermonde nets with a view to obtain digital nets that serve as stepping stones for new constructions of digital sequences called Vandermonde sequences. Another new family of Vandermonde sequences is built from global function fields, and this family of digital sequences has asymptotically optimal quality parameters for a fixed prime-power base and increasing dimension.

Keywords

  • Low-discrepancy point sets and sequences
  • \((t, m, s)\)-nets
  • \((t, s)\)-sequences
  • Digital point sets and sequences

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  • DOI: 10.1007/978-3-319-33507-0_3
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Acknowledgments

The first author was supported by the Austrian Science Fund (FWF), Project F5505-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.

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Correspondence to Harald Niederreiter .

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Hofer, R., Niederreiter, H. (2016). Vandermonde Nets and Vandermonde Sequences. In: Cools, R., Nuyens, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-319-33507-0_3

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