On the Lattice Structure of Certain Linear Congruential Sequences Related to AWC/SWB Generators
Raymond Couture, Pierre L’Ecuyer · Mathematics of Computation · 1994
We analyze the lattice structure of certain types of linear congruential generators (LCGs), which include close approximations to the add-with-carry and subtract-with-borrow (AWC/SWB) random number generators introduced by Marsaglia and Zaman, and also to combinations of the latter with ordinary LCGs. It follows from our results that all these generators have an unfavorable lattice structure in large dimensions.