L’Ecuyer, Pierre; Tezuka, Shu Structural properties for two classes of combined random number generators. (English) Zbl 0748.65007 Math. Comput. 57, No. 196, 735-746 (1991). A linear congruential generator (LCG) is a recurrence: \(s_ i=as_{i- 1}\mod m\). Such generators have a drawback: When you plot the points \((s_ i,s_{i+1})\) on the plane you obtain a “lattice structure” — all points lie on easily discernible equidistant vertical lines, and also on equidistant horizontal lines. One way of getting rid of such a regularity is to apply a set of LCGs with distinct prime moduli.In the paper two such generators are considered. It is shown that such combined generators may be in many cases effectively approximated by an LCG which has a modulus equal to the product of the moduli of the individual components. Thus constructing a combined generator is an efficient way of implementing an LCG with much larger modulus than the largest integer representable on the target computer.The result of the paper supplies also the theoretical tool for studying such combined generators. Reviewer: P.Staniewski (Warszawa) Cited in 1 ReviewCited in 15 Documents MSC: 65C10 Random number generation in numerical analysis Keywords:random number generator; linear congruential generator; combined generators Software:AS 183 PDFBibTeX XMLCite \textit{P. L'Ecuyer} and \textit{S. Tezuka}, Math. Comput. 57, No. 196, 735--746 (1991; Zbl 0748.65007) Full Text: DOI