[EDIT] This post was migrated from my blog from 2011…
This is a classic subject in numerical (Monte Carlo) integration.
Uniform 2D distribution vs. Halton series for the first 2 dimensions
To the left: 32768 points in a 512×512 image using a uniform random number generator (Mersenne Twister). To the right, the first 32768 pairs in the Halton series, using dimensions #0 and #1. Click to enlarge!