Mersenne Twister - k-distribution

k-distribution

A pseudorandom sequence x_i of w-bit integers of period P is said to be k-distributed to v-bit accuracy if the following holds.

Let trunc_v(x) denote the number formed by the leading v bits of x, and consider P of the kv-bit vectors

.

Then each of the 2kv possible combinations of bits occurs the same number of times in a period, except for the all-zero combination that occurs once less often.