LOWER BOUNDS FOR THE DISCREPANCY OF TRIPLES OF INVERSIVE CONGRUENTIALPSEUDORANDOM NUMBERS WITH POWER OF 2-MODULUS

This paper deals with the inversive congruential method with Fewer of two modulus m for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that there exist parameters in the inversive congruential met hod such that the discrepancy of the corresponding point sets in the u nit cube is of an order of magnitude at least m(-1/3). The method of p roof relies on a detailed analysis of certain rational exponential sum s.