Here we don't want to go into a detailed discussion.
For detail, please consult with the preprint
Briefly saying, MT is designed according to the modern researches
on the practical conditions which a generator should satisfy.
We don't have a practical definition of "good pseudorandomness"
for pseudorandom number generators yet now.
So, there is no rigourous mathematical assurance for MT to be
a defect-free random number generators.
However, it is widely believed that the spectral test is one
of the strongest test to select a good generator.
MT is designed to pass a similar test, called the k-distribution test.
For example, if we look the output with 32-bit accuracy, then
the 623-tuples from the output in a whole period are equidistributed in
the 623-dimensional unit cube.
For 16-bit accuracy, 1246-tuples are equidistributed in 1246-dimension,
and for 2-bit accuaracy, in 9968-dimension. These values are at least
15 times larger than the previous records.
MT passed many stringent tests, including the diehard test by G.Marsaglia
and the load test by P.Hellekalek and S.Wegenkittl.
MT is an improved version of a very successful generator TT800,
which has the period 2^800-1
and has been used for a few years with favorable comments
by many users. MT is much more robust.
The generator is implemented to generate the output only by
fastest arithmetic operations: no division, no multiplication.
By generating an array at one time, it takes the full advantage
of cache memory and pipeline processing.