halton, a Python code which computes elements of a Halton Quasi Monte Carlo (QMC) sequence using a simple interface.

The standard M-dimensional Halton sequence is simply composed of M 1-dimensional van der Corput sequences, using as bases the first M primes.

The HALTON function will return the M-dimensional element of this sequence with index I.

The HALTON_SEQUENCE function will return the M-dimensional elements of this sequence with indices I1 through I2.

The HALTON_INVERSE function accepts an M-dimensional value, presumably computed by HALTON, and returns its original index I.

The HALTON_BASE function allows the user to replace the standard basis of primes with some other choice.


The computer code and data files described and made available on this web page are distributed under the MIT license


halton is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

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  1. John Halton,
    On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals,
    Numerische Mathematik,
    Volume 2, 1960, pages 84-90.
  2. John Halton, GB Smith,
    Algorithm 247: Radical-Inverse Quasi-Random Point Sequence,
    Communications of the ACM,
    Volume 7, 1964, pages 701-702.
  3. Ladislav Kocis, William Whiten,
    Computational Investigations of Low-Discrepancy Sequences,
    ACM Transactions on Mathematical Software,
    Volume 23, Number 2, 1997, pages 266-294.

Source Code:

Last revised on 02 October 2016.