Random number generators based on linear recurrences modulo 2 are widely used and appear in different forms, such as the simple and combined Tausworthe generators, the GFSR, and the twisted GFSR, generators. Low-discrepancy point sets for quasi-Monte Carlo integration can also be constructed based on these linear recurrences. The quality of these generators or point sets is usually measured by certain equidistribution criteria. Combining two or more recurrences and adding linear output transformations can be used to improve the equidistribution properties.
In this paper, we explore the combination of recurrences of different types, together with different kinds of linear output transformations. We have developed flexible software tools to make computer searches for good generators with respect to equidistribution criteria that consider selected low-dimensional projections. We provide several examples of search results.