Tables of linear congruential generators of different sizes and good lattice structure

Abstract

We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ℓ = 8 , 9 , … , 64 , 127 , 128 \ell = 8, 9, \dots , 64, 127, 128 , we take as a modulus m m the largest prime smaller than 2 ℓ 2^\ell , and provide a list of multipliers a a such that the MLCG with modulus m m and multiplier a a has a good lattice structure in dimensions 2 to 32. We provide similar lists for power-of-two moduli m = 2 ℓ m = 2^{\ell } , for multiplicative and non-multiplicative LCGs.