ON THE DISTRIBUTION OF COUNTER-DEPENDENT NONLINEAR CONGRUENTIAL PSEUDORANDOM NUMBER GENERATORS IN RESIDUE RINGS.

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, using a technique developed by Niederreiter and Shparlinski, we present discrepancy bounds for sequences of s-tuples of successive pseudorandom numbers generated by counter-dependent generators modulo a composite M. [ABSTRACT FROM AUTHOR]