page_title: Low-discrepancy sequence
section_title: Graphical examples
hierarchical_section_title: Low-discrepancy sequence / Graphical examples
context_page_description: In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x₁, ..., xN has a low 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 of B, as would happen on average in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice of B and how the discrepancy for every B is computed and combined.
  Low-discrepancy sequences are also called quasirandom sequences, due to their common use as a replacement of uniformly distributed 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.
context_section_description: The points plotted below are the first 100, 1000, and 10000 elements in a sequence of the Sobol' type.
  For comparison, 10000 elements of a sequence of pseudorandom points are also shown.
  The low-discrepancy sequence was generated by TOMS algorithm 659.
  An implementation of the algorithm in Fortran is available from Netlib.
caption: The first 1000 points in the same sequence. These 1000 comprise the first 100, with 900 more points.
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