Dimensionality of Spectral Test for a Linear Congruential Random Number Generator

Abstract

This paper considers the successive dimensions of the spectral test for a linear congruential generator (LCG) based on three types of the upper bound on the center density. We conduct an exhaustive search for the maximum and difference normalized spectral value in dimensions 2, 3, …, 32 of an LCG. The experimental result indicates that the appropriate dimensions for implementing the spectral test are 2, 3, …, 8 with the objective of maximizing the normalized spectral value.