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Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
Abstract
An algorithm to generate Sobol' sequences to approximate integrals in up to 40 dimensions has been previously given by Bratley and Fox in Algorithm 659. Here, we provide more primitive polynomials and "direction numbers" so as to allow the generation of Sobol' sequences to approximate integrals in up to 1111 dimensions. The direction numbers given generate Sobol' sequences that satisfy Sobol's so-called Property A.
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“The Sobol sequence is a lowdiscrepancy sequence constructed using binary digits and designed so that the points are distributed evenly in the unit hypercube.”
From Doubly blocked variant of Genz’s method for multivariate normal integration (2026) · cites this paper as Joe and Kuo (2003)
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On the distribution of points in a cube and the approximate evaluation of integrals
Sobol', I. M. (1967) · USSR Computational Mathematics and Mathematical Physics · doi:10.1016/0041-5553(67)90144-9 · Cited by 2,975
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Cited by
Berg, J., & Nyström, K. (2018) · Neurocomputing · doi:10.1016/j.neucom.2018.06.056 · Cited by 657
An Introduction to Computational Stochastic PDEs
Lord, G. J., Powell, C. E., & Shardlow, T. (2014) · Cambridge University Press eBooks · doi:10.1017/cbo9781139017329 · Cited by 537
Doubly blocked variant of Genz’s method for multivariate normal integration
Peterlin, J. (2026) · Computational Statistics · doi:10.1007/s00180-026-01794-8
Metadata
- Authors
- Joe, S., & Kuo, F. Y.
- Venue
- ACM Transactions on Mathematical Software
- Published
- 2003-03
- Volume
- 29
- Issue
- 1
- Pages
- 49-57
- ISSN
- 0098-3500
- 1557-7295
- Cited by
- 346
- References
- 1
- Language
- en
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