New Perspectives on (0,s)-Sequences

Christiane Lemieux () and Henri Faure
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Christiane Lemieux: University of Waterloo, Department of Statistics and Actuarial Science

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 113-130 from Springer

Abstract: 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.

Keywords: Generate Matrice; Brownian Bridge; Direction Number; Digital Sequence; Pairwise Coprime (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_7

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DOI: 10.1007/978-3-642-04107-5_7

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