Upper bounds in spectral test for multiple recursive random number generators with missing terms

One method for generating random numbers (RNs) of long period recommended by many scholars is the multiple recursive generator (MRG), in that the current RN is essentially a linear combination of the Ic preceding ones. In this paper, the upper bounds for a figure of merit adopted in the spectral test are derived for the k(th) order MRG with p less than or equal to k terms. As p gets smaller, the bounds become smaller as well. The simplest form of the k(th) order MRG with two terms frequently discussed in literature is found to have the worst bound.