Maximally equidistributed pseudorandom number generators via linear output transformations

This article discusses construction of maximally equidistributed (ME) linear feedback shift register generators by using linear output transformations. We introduce a new strategy to find linear output transformations attaining the ME property, and apply it to the WELL generators and the Mersenne Twister. As a result, we found a modified version of the WELL generators with the ME property, having fewer operations than the original ME WELL generators. We also found a ME Mersenne Twister which is faster than the WELL generators with a period of $2^{19937}‐1$ on some platforms. The C codes of the obtained generators are available at %http://www3.ocn.ne.jp/%7Eharase/megenerators.html.