An analysis of linear congruential random number generators when multiplier restrictions exist

This research conducts an exhaustive search for the best spectral test performance in a full period linear congruential generator (LCG) with the largest prime modulus smaller than 2^b, for bit sizes b = 8, 9, … , 31. Three types of restrictions on multipliers are presented and some full period LCGs are presented for use in three different spectral test dimensions. According to the exhaustive searches we perform, the results indicate differences exist among the numbers of possible multipliers for the three types of multiplier restrictions. We demonstrate that these differences can affect the performance of spectral tests for different dimensions.