On the distribution of pseudo-random numbers generated by the linear congruential method. III

Harald Niederreiter
1976 Mathematics of Computation  
The discrepancy of a sequence of pseudo-random numbers generated by the linear congruential method, both homogeneous and inhomogeneous, is estimated for parts of the period that are somewhat larger than the square root of the modulus. The analogous problem for an arbitrary linear congruential generator modulo a prime is also considered, the result being particularly interesting for maximal period sequences. It is shown that the discrepancy estimates in this paper are best possible apart from
more » ... sible apart from logarithmic factors.
doi:10.1090/s0025-5718-1976-0457392-1 fatcat:amsakiyevfcophdq5fobtjnlxy