In quasi-Monte Carlo, there is a rather strong notion "completely uniformly distributed" sequences, which somehow mimics independence and is described, for example, at the end of this post.
While the theory is clear to me, how do we practically generate such sequences? I can't find a reference, but I think I've heard that we can construct such a sequence from a low-discrepancy sequence (like a Sobol sequence) by random permutation of the indices?
Does anybody have a reference at hand or can briefly describe an easy-to-implement method to produce them?
EDIT: I know that there is the paper of Levin, but the construction described is rather complex. Especially in high dimension (I'm interested in a dimension around 40 at least), this seems to be hard to implement.
