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 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 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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