Comment by johnnymellor

Yes, it's a very desirable trait in https://en.m.wikipedia.org/wiki/Quasi-Monte_Carlo_method

Quasi-Monte Carlo has a rate of convergence close to O(1/N), whereas the rate for the Monte Carlo method is O(N^(−0.5))

For such applications it's best to use quasi-random numbers (a.k.a. low-discrepancy sequences) such as the Halton sequence or the Sobol sequence instead of pseudorandom numbers.