On the Lattice Structure of a Special Class of Multiple Recursive Random Number Generators

We examine some properties of the points produced by certain classes of long-period linear multiple recursive random number generators proposed by L.-Y. Deng and his co-authors in several papers. These generators have their parameters selected in special ways to make the implementation faster. We show that as a result, the points produced by these generators have a poor lattice structure, and a poor initialization of the state can have long-lasting impact, because of the limited diffusion capacity of the recurrence.