manuscripta mathematica

, Volume 55, Issue 3–4, pp 455–465

The sub-lattice structure of linear congruential random number generators

  • Lothar Afflerbach

DOI: 10.1007/BF01186658

Cite this article as:
Afflerbach, L. Manuscripta Math (1986) 55: 455. doi:10.1007/BF01186658


Sequences of pseudo-random numbers are discussed which are generated by the linear congruential method where the period is equal to the modulus m. Such sequences are divided into non-overlapping vectors with n components. In this way for each initial number exactly m/gcd(n, m) different vectors are obtained. It is shown that the periodic continuation (with period m) of these vectors forms a grid which is a sub-grid of the familiar grid generated by all m overlapping vectors. A sub-lattice structure also exists for certain multiplicative congruential generators which are often used in practice.

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Lothar Afflerbach
    • 1
  1. 1.Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtFederal Republic of Germany

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