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New Perspectives on (0,s)-Sequences

In: Monte Carlo and Quasi-Monte Carlo Methods 2008

Author

Listed:
  • Christiane Lemieux

    (University of Waterloo, Department of Statistics and Actuarial Science)

  • Henri Faure

Abstract

Low-discrepancy sequences that have an optimal value of 0 for their t -parameter have always been of interest to both theorists and practitioners. However, in practice the Sobol’ sequence often performs better than the original (0,s)-sequences in prime bases proposed by Faure in 1982, although the former construction does not have an optimal value of 0 for its t-parameter. In this paper, we introduce new ideas that can be used to find improved constructions for (0,s)-sequences in prime bases. To do so, we study them within the framework of generalized Niederreiter sequences, which was introduced by Tezuka in 1993. We take a closer look at the structure of the corresponding generating matrices, as this helps us to better understand the differences and analogies between the constructions that we are interested in. This study is then used to guide our search for improved (0,s)-sequences, which are shown to perform well on a variety of problems.

Suggested Citation

  • Christiane Lemieux & Henri Faure, 2009. "New Perspectives on (0,s)-Sequences," Springer Books, in: Pierre L' Ecuyer & Art B. Owen (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 113-130, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04107-5_7
    DOI: 10.1007/978-3-642-04107-5_7
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