Selection Criteria for (Random) Generation of Digital (0,s)-Sequences

Henri Faure ()
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Henri Faure: UMR 6206 CNRS, Institut de Mathématiques de Luminy

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 113-126 from Springer

Abstract: Summary Digital (0, s)-sequences in an arbitrary prime base b ≥ s may be randomly scrambled in various ways. Simple and widely used scramblings are obtained by multiplying on the left the upper triangular generator matrices by nonsingular lower triangular (NLT) matrices whose entries are randomly chosen in the set of digits Zb={0, 1, …, b − 1 [Tez94]. From our recent results [Fau05], we are able to propose subsets of Zb of various sizes for the random selection of the entries of the NLT matrices above. Moreover, since multiplications are permutations, our selection criteria are part of the general framework of Owen [Owe95] and may be applied to any kind of digital sequences, like Halton or Niederreiter sequences.

Date: 2006
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DOI: 10.1007/3-540-31186-6_8

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