Editing Low-discrepancy sequence (section)

{{Short description|Type of mathematical sequence}}
In [[mathematics]], a '''low-discrepancy sequence''' is a [[sequence]] with the property that for all values of <math>N</math>, its subsequence <math>x_1, \ldots, x_N</math> has a low [[discrepancy of a sequence|discrepancy]].

Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an arbitrary set ''B'' is close to proportional to the [[Measure (mathematics)|measure]] of ''B'', as would happen on average (but not for particular samples) in the case of an [[equidistributed sequence]]. Specific definitions of discrepancy differ regarding the choice of ''B'' ([[hyperspheres]], [[Hypercube|hypercubes]], etc.) and how the discrepancy for every B is computed (usually normalized) and combined (usually by taking the worst value).

Low-discrepancy sequences are also called '''quasirandom''' sequences, due to their common use as a replacement of uniformly distributed [[random sequence|random numbers]].
The "quasi" modifier is used to denote more clearly that the values of a low-discrepancy sequence are neither random nor [[pseudorandom]], but such sequences share some properties of random variables and in certain applications such as the [[quasi-Monte Carlo method]] their lower discrepancy is an important advantage.