An approximate spectral test for full period two-term third-order multiple recursive generators

Abstract

This paper considers the problem of searching for a vector of multipliers in a full period two-term third-order multiple recursive generator (3MRG) with the objective of maximizing the spectral test performance. An approximate spectral test by considering the basis reduction is proposed. Sixteen variants of the approximate spectral test are evaluated by ten performance measures and running time. The spectral value found by the backward heuristic with approximate spectral test is superior to the best previously published one for the full period 3MRG.