We examine how a statistical test based on discrete spacings between points, in one or more dimensions, detects the regularities in certain popular classes of random number generators. We provide a rule of thumb giving the minimal sample size for the test to reject the generator systematically,...

Most random number generators used in practice are based on linear recurrences, with linear output transformations. This gives long periods, fast implementations, and structures that are easy to analyze. But the points produced by these generators have very regular structures. Nonlinear...