RANDOM NUMBERS FALL MAINLY IN THE PLANES

Most of the worlds computer centers use congruential random number generators. This note points out that such random number generators produce points in 2,3,4,... dimensions which are too regular for many Monte Carlo calculations. The trouble is that the points fall exactly on a lattice with quite a gross structure. The paper gives details of the degree of regularity of such generators in terms of sets of relatively few parallel hyperplanes which contain all of the points produced by the generator.