Whilst reading up on Xorshift I came across the following (emphases added):
The following xorshift+ generator, instead, has 128 bits of state, a maximal period of 2^128 − 1 and passes BigCrush:
This generator is one of the fastest generator passing BigCrush; however, it is only 1-dimensionally equidistributed.
Earlier in the article there's the following:
Both generators, as all xorshift* generators of maximal period, emit a sequence of 64-bit values that is equidistributed in the maximum possible dimension.
What does it mean for a sequence to be equidistributed in one dimension vs. multiple dimensions vs. not at all?