Abstract.
The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present a new bound on the s-dimensional discrepancy of nonlinear congruential pseudorandom numbers over the residue ring \({\Bbb Z}_M\) modulo M for an “almost squarefree” integer M. It is useful to recall that almost all integers are of this type. Moreover, if the generator is associated with a permutation polynomial over \({\Bbb Z}_M\) we obtain a stronger bound “on average” over all initial values. This bound is new even in the case when M = p is prime.
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El-Mahassni, E., Shparlinski, I. & Winterhof, A. Distribution of Nonlinear Congruential Pseudorandom Numbers Modulo Almost Squarefree Integers. Mh Math 148, 297–307 (2006). https://doi.org/10.1007/s00605-005-0355-7
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DOI: https://doi.org/10.1007/s00605-005-0355-7