Quadratic congruential pseudorandom numbers: Distribution of lagged pairs

The present paper deals with the quadratic congruential method with power of two modulus for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences (xn)n⩾0 are studied based on the distribution of lagged pairs (xn,xn+2). Upper and lower bounds for the discrepancy of the corresponding point sets in the unit square are established.