Latin Random Squares in M dimensions

LATIN_RANDOM is a FORTRAN90 library which makes Latin random squares.

A Latin square is a selection of one point from each row and column of a square matrix or table. In M dimensions, the corresponding item is a set of N points, where, in each dimension, there is exactly one point whose coordinates are in a given "column" or range of values. To emphasize the use of higher dimensions, these objects are sometimes called Latin hypersquares.

A Latin Random Square (I just made up this name) is a set of N points, where one point is taken at random from each of the subsquares of a Latin Square. These points may be regarded as an M dimensional quasirandom pointset.


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


LATIN_RANDOM is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

LATIN_RANDOM_DATASET, a FORTRAN77 program which computes a Latin Hypercube in M dimensions of N points, randomly placed within their subsquares.

NORMAL, a FORTRAN77 library which computes elements of a sequence of pseudorandom normally distributed values.

UNIFORM, a FORTRAN77 library which computes elements of a uniform pseudorandom sequence.


  1. Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Springer Verlag, pages 201-202, 1983.
  2. C J Colbourn and J H Dinitz,
    CRC Handbook of Combinatorial Design,
    CRC, 1996.
  3. Bennett Fox,
    Algorithm 647:
    Implementation and Relative Efficiency of Quasirandom Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, pages 362-376, 1986.
  4. Michael McKay, William Conover, Richard Beckman,
    A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,
    Volume 21, pages 239-245, 1979.
  5. Albert Nijenhuis, Herbert Wilf,
    Combinatorial Algorithms,
    Academic Press, 1978, second edition,
    ISBN 0-12-519260-6.
  6. Herbert Ryser,
    Combinatorial Mathematics,
    Mathematical Association of America, 1963.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 14 December 2009.