Quasi-random sequences for numerical integration

What are low-discrepancy (quasi-random) numbers and why are they used?

Deterministic point sets that fill space more evenly than random draws. Sequences such as Halton, Sobol and Faure place each new point in the gaps left by earlier ones, so integration error is close to $O((\log N)^d/N)$ instead of Monte Carlo's $O(N^{-1/2})$. They speed up option pricing by simulation, though gains fade in very high dimensions unless the important dimensions come first (e.g. Brownian bridge), and error bars need randomised versions.