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Mathematics of Computation

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The lattice structure of multiplicative congruential pseudo-random vectors

Authors: W. A. Beyer, R. B. Roof and Dorothy Williamson
Journal: Math. Comp. 25 (1971), 345-363
MSC: Primary 65C10
Corrigendum: Math. Comp. 65 (1996), 445-446.
MathSciNet review: 0309263
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Abstract: The lattice structure of points in an n-dimensional space produced by an appropriate grouping of pseudo-random numbers obtained from multiplicative congruential generators is discussed. Examples are given for $2 \leqq n \leqq 6$. The work is based on the theory of the reduction of positive quadratic forms in n variables.

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Keywords: Multiplicative congruential pseudo-random numbers, Lehmer pseudo-random numbers, Monte Carlo integration, random numbers, lattices of random points, testing of random numbers, reduced cells, positive quadratic forms, quadratic forms
Article copyright: © Copyright 1971 American Mathematical Society