On the Statistical Independence of Compound Pseudorandom Numbers Over Part of the Period

This article deals with the compound methods with modulus m for generating uniform pseudorandom numbers, which have been introduced recently. Equidistribution and statistical independence properties of the generated sequences over part of the period are studied based on the discrepancy of d-tuples of successive pseudorandom numbers. It is shown that there exist parameters in compound methods such that the discrepancy over part of the period of the corresponding point sets in the d-dimensional unit cube is of an order magnitude of O(N^-1/2(log N)^d+3) for all N = 1,..., m. This result is applied to the compound nonlinear, inversive and explicit inversive congruential methods.