Average Discrepancy, Hyperplanes, and Compound Pseudorandom Numbers

This paper deals with compound nonlinear congruential methods for generating uniform pseudorandom numbers. The average equidistribution and statistical independence behavior of the generated sequences over arbitrary parts of the period is studied, based on the average value of the discrepancy of certain point sets. General upper bounds for these average values are established, which depend on the number of points on certain hyperplanes over finite fields. These bounds are applied to the compound explicit inversive congruential method, which has been introduced recently.