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On the distribution of pseudo-random numbers generated by the linear congruential method. III

Author: Harald Niederreiter
Journal: Math. Comp. 30 (1976), 571-597
MSC: Primary 10K05; Secondary 65C10
MathSciNet review: 0457392
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Abstract: The discrepancy of a sequence of pseudo-random numbers generated by the linear congruential method, both homogeneous and inhomogeneous, is estimated for parts of the period that are somewhat larger than the square root of the modulus. The analogous problem for an arbitrary linear congruential generator modulo a prime is also considered, the result being particularly interesting for maximal period sequences. It is shown that the discrepancy estimates in this paper are best possible apart from logarithmic factors.

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Keywords: Pseudo-random numbers, discrepancy, equidistribution test, trigonometric sums, linear recurring sequences, maximal period sequences
Article copyright: © Copyright 1976 American Mathematical Society

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