Comment by freehorse

And why does it matter in the context of randomly assigning participants in an experiment into groups? It is not plausible that any theoretical "gaps" in the pseudorandomness are related to the effect you are trying to measure, and unlikely that there is a "pattern" created in how the participants get assigned. You just do one assignment. You do not need to pick a true random configuration, just one random enough.

I assume that as long as p-values are concerned, the issue raised could very well be measured with simulations and permutations. I really doubt though that the distribution of p-values from pseudorandom assignments with gaps would not converge very fast to the "real" distribution you would get from all permuations due to some version of a law of large numbers. A lot of resampling/permutation techniques work by permuting a negligible fraction of all possible permutations, and the distribution of the statistics extracted converges pretty fast. As long as the way the gaps are formed are independent of the effects measured, it sounds implausible that the p-values one gets are problematic because of them.