Nonlinear congruential pseudorandom number generators can have unexpectedly short periods. Shamir and Tsaban introduced the class of counter-dependent generators which admit much longer periods. In this paper we present a discrepancy bound for sequences of s-tuples of successive pseudorandom numbers generated by counter-dependent generators and a lower bound on their linear complexity.

pseudorandom numbers, nonlinear congruential method, discrepancy, exponential sums.