32-bit multipliers for linear congruential random number generators

This paper conducts an exhaustive search for the maximum spectral test in a full period Linear Congruential Generator (LCG) with modulus 2(32) - 5. We consider three types of multiplier: unrestricted multiplier, approximate factoring restriction on multiplier, and double precision floating point restriction on multiplier. According to propositions reported in Tang (2003, 2005), three fourths of the multipliers are reduced. Some good LCGs are presented to satisfy the different requirements of today's computer simulation studies.