quasi random number sequences [1] are "space filling". A typical problem of sampling from the uniform distribution is that parts of the space never get sampled due to sampling bias. Quasi-random sequences ensure evenish distribution. This speeds up many sampling based algorithms e.g. MCMC, by an order of a complexity level.

I too believe random numbers are usually the wrong choice.

[1] http://www.mathworks.co.uk/help/stats/generating-quasi-rando...