Optimization of random number generators: efficient search for high-quality LCGs

In this work we will discuss how to optimize multipliers for prime-modulus linear congruential pseudo-random number generators with respect to the spectral test. The optimization efficiency has shown itself to be strongly dependent on the encoding strategy for the multipliers within the random search process. The optimal encoding technique will be demonstrated to be a representation in terms of powers of a primitive root. A sample distributed large-scale parameter search for subsequence stable LCGs will be conducted using the developed concepts.