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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Tables of linear congruential generators of different sizes and good lattice structure
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by Pierre L’Ecuyer PDF
Math. Comp. 68 (1999), 249-260 Request permission


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
  • Email:
  • 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.
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 249-260
  • MSC (1991): Primary 65C10
  • DOI:
  • MathSciNet review: 1489972