[contravariant]

If the number of dimensions is high enough then pretty much all points are far away from each other so there's no real need to worry about points clustering. You're at a much greater risk of simply missing interesting parts of your space than you are of oversampling any part of it.

[blake1]

This can be especially bad if one corner hides a catastrophe. Any automatic method is likely to have an exponential struggle to sample appropriately. At a certain point, you just need to apply your own understanding of the problem you are trying to solve, and resort to an ad hoc method to do the “right” thing.

[pmiller2]

That's exactly the problem QMC methods solve. By choosing a sequence of sample points of low discrepancy, you make sure to sample the entire space as evenly as possible.

[contravariant]

It does but if you've got 100s of dimensions then you have no hope of ever sampling anything close to the entire space. Even if you just pick 2 points per dimension you've got no way of trying every combination.