ORBITS AND LATTICES FOR LINEAR RANDOM NUMBER GENERATORS WITH COMPOSITE MODULI

In order to analyze certain types of combinations of multiple recursiv e linear congruential generators (MRGs), we introduce a generalized sp ectral test. We show how to apply the test in large dimensions by a re cursive procedure based on the fact that such combinations are subgene rators of other MRGs with composite moduli. We illustrate this with th e well-known RANMAR generator. We also design an algorithm generalizin g the procedure to arbitrary random number generators.