Subrandom numbers

I was surfing Wikipedia one night when I came across the page on low-discrepancy sequences, or subrandom numbers. These are sequences designed to cover the maximum "area" possible in a given range. They appear to be useful in situations which don't require randomness as much as they require even spacing between numbers, like quasi-Monte Carlo simulations.

This prompted me to wonder what it is exactly about random numbers that makes them suited for generating test data. Random numbers are prone to clustering and gaps, in a way which seems, to me, to be disadvantageous for property-based testing. Despite this, I asked around, and I wasn't able to find a case of subrandom numbers being used for property-based testing. Is this something anyone here has tried? Is it worth adding to property-based testing libraries? It should require fairly few changes for monadic varieties.

No files, tests, or entry points are named. Start by reading the linked low-discrepancy-sequence background and examining how QuickCheck generates test data, including the monadic varieties mentioned. Done would require a concrete implementation scope and tests, neither of which this exploratory issue currently specifies.