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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Tables of linear congruential generators
of different sizes and good lattice structure

Author: Pierre L'Ecuyer
Journal: Math. Comp. 68 (1999), 249-260
MSC (1991): Primary 65C10
MathSciNet review: 1489972
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Abstract: We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For $\ell = 8, 9, \dots, 64, 127, 128$, we take as a modulus $m$ the largest prime smaller than $2^\ell$, and provide a list of multipliers $a$ such that the MLCG with modulus $m$ and multiplier $a$ has a good lattice structure in dimensions 2 to 32. We provide similar lists for power-of-two moduli $m = 2^{\ell}$, for multiplicative and non-multiplicative LCGs.

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Additional Information

Pierre L'Ecuyer
Affiliation: Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada

Keywords: Random number generation, linear congruential, lattice structure, spectral test
Received by editor(s): May 9, 1997
Additional Notes: This work has been supported by NSERC-Canada grants ODGP0110050 and SMF0169893, and FCAR-Québec grant 93ER1654. Thanks to Raymond Couture, Peter Hellekalek, and Harald Niederreiter for useful suggestions, to Ajmal Chaumun who helped in computing the tables, and to Karl Entacher who pointed out an error in an earlier version.
Article copyright: © Copyright 1999 American Mathematical Society