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Admissible and Asymptotically Optimal Linear Congruential Generators

The paper is devoted to the theoretical study of the so-called spectral test for Linear Congruential Generators (briefly, LCGs) of pseudorandom numbers with moduli 2 p and full periods. Using the technique developed in V. Gerlovina and V. Nekrutkin, Monte Carlo Methods and Appl. 11:2, 2005, we present several examples of admissible and asymptotical optimal sequences of multiplicators. These examples give rise to well-directed search methods for LCGs with good equidistribution properties.