Maybe others have already solved this algorithm in cool ways. Perhaps there's some prior art on this that can be referenced...
People have done work on something called "quasi-random" sampling in the context of Monte-Carlo integration. The idea is that the integral should converge faster if the sample points are spread out more evenly than would happen by random. Numerical Recipies has a section on the subject or try the following Google searches:
It doesn't really deal with random permutations, but I suspect that if you did a 2d quasi-random sequence and looked at the x-rank vs. the y-rank you'd get something interesting.
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