manuscripta mathematica

, Volume 62, Issue 2, pp 245–248 | Cite as

On Marsaglia's lattice test for pseudorandom numbers

  • Jürgen Eichenauer
  • Harald Niederreiter


Nonlinear recursive congruential pseudorandom number generators with prime modulus and maximal period length are considered. Those generators are characterized which behave optimally with respect to Marsaglia's lattice test. An example for an extremely bad generator with this property is given, which demonstrates the weakness of this test.


Number Theory Number Generator Algebraic Geometry Topological Group Period Length 
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  1. [1]
    Eichenauer, J; Grothe, H. and Lehn, J.: Marsaglia's lattice test and non-linear congruential pseudo random number generators, Metrika (to appear)Google Scholar
  2. [2]
    Marsaglia, G.: The structure of linear congruential sequences. In: Zaremba, S.K. (Ed.) Applications of number theory to numerical analysis, Academic Press, New York, 249–285 (1972)Google Scholar
  3. [3]
    Niederreiter, H.: Remarks on nonlinear congruential pseudorandom numbers, Metrika (to appear)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Jürgen Eichenauer
    • 1
  • Harald Niederreiter
    • 2
  1. 1.Fachbereich MathematikTechnische HochschuleDarmstadt
  2. 2.Kommission für MathematikÖsterr. Akad. d. Wiss.Wien

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