A quasirandom sequence is a sequence of 
-tuples that fills n-space
more uniformly than uncorrelated random points, sometimes also called a low-discrepancy
sequence. Although the ordinary uniform random numbers and quasirandom sequences
both produce uniformly distributed sequences, there is a big difference between the
two. A uniform random generator on 
will produce outputs so that each trial has the same probability
of generating a point on equal subintervals, for example 
and 
. Therefore, it is possible for 
trials to coincidentally all lie in the first half of the
interval, while the 
st point still falls within the other of the two halves
with probability 1/2. This is not the case with the quasirandom sequences, in which
the outputs are constrained by a low-discrepancy requirement that has a net effect
of points being generated in a highly correlated manner (i.e., the next point "knows"
where the previous points are).
Quasirandom sequences supply the deterministically chosen sample points used in quasi-Monte Carlo methods.
Such a sequence is extremely useful in computational problems where numbers are computed on a grid, but it is not known in advance how fine the grid must be to obtain accurate results. Using a quasirandom sequence allows stopping at any point where convergence is observed, whereas the usual approach of halving the interval between subsequent computations requires a huge number of computations between stopping points.
