Efficient spectral tests for multiple recursive generators

Large-order maximum-period Multiple Recursive Generators (MRGs) have become popular in the area of computer simulation. They have the nice properties of high-dimensional equi-distribution, generating efficiency, long period, and portability. The spectral test is a commonly used criterion for ranking pseudo-random number generators. Procedures for computing the spectral test values of MRGs are available in the literature but may not be efficient when the order of the MRG is large. In this article, we propose a novel method for the spectral test computation of MRGs that is simple, intuitive, and particularly efficient for MRGs with few non zero terms. With the proposed method, we are able to provide a list of ready-to-use "better" generators with respect to the spectral test performance among the DX generators of order k for various values of k.