NIEDERREITER2
Niederreiter Quasirandom Datasets
Base = 2

NIEDERREITER2 is a dataset directory which contains points generated by the M-dimensional Niederreiter sequence using a base of 2.

The datasets are distinguished by the values of the following parameters:

• M, the spatial dimension;
• N, the number of points to generate;
• BASE, which is always 2 for these datasets;
• SKIP, the initial number of points to skip over;

A nonzero value of SKIP may be specified, to allow the sequence to "warm up". In this case, a recommended value is BASE**12 = 4096.

Licensing:

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

Related Data and Programs:

NIEDERREITER2, a C++ library which computes elements of a Niederreiter quasirandom sequence using base 2.

NIEDERREITER2_DATASET, a FORTRAN90 program which allows the user to define and compute a Niederreiter2 dataset.

PLOT_POINTS, a FORTRAN90 program which can plot two dimensional datasets, making Encapsulated PostScript images.

TABLE, a file format which is used to store the datasets.

TABLE_TOP, a FORTRAN90 program which can be used to analyze datasets of any dimension, by creating images of pairwise coordinates.

Example dataset:

A typical (but small) dataset looks like this:

#  niederreiter2_02_00010.txt
#  created by NIEDERREITER2_DATASET.
#
#  File generated on March 19 2003  11:38:30.446 AM
#
#  Spatial dimension M =      2
#  Number of points N =     10
#  Base:      2
#  Initial values skipped =   4096
#
  0.000366  0.470581
  0.500366  0.970581
  0.750366  0.220581
  0.250366  0.720581
  0.375366  0.095581
  0.875366  0.595581
  0.625366  0.345581
  0.125366  0.845581
  0.187866  0.158081
  0.687866  0.658081
      

Reference:

1. Paul Bratley, Bennett Fox, Harald Niederreiter,
   Algorithm 738:
   Programs to Generate Niederreiter's Low-Discrepancy Sequences,
   ACM Transactions on Mathematical Software,
   Volume 20, Number 4, pages 494-495, 1994.
2. Harald Niederreiter,
   Low-discrepancy and low-dispersion sequences,
   Journal of Number Theory,
   Volume 30, 1988, pages 51-70.

Datasets:

Datasets in M = 2 dimensions include:

• niederreiter2_02_00010.txt, M = 2, N = 10, BASE = 2, SKIP = 4096;
• niederreiter2_02_00010.png, a PNG image of the dataset;
• niederreiter2_02_00100.txt, M = 2, N = 100, BASE = 2, SKIP = 4096;
• niederreiter2_02_00100.png, a PNG image of the dataset;
• niederreiter2_02_01000.txt, M = 2, N = 1000, BASE = 2, SKIP = 4096;
• niederreiter2_02_01000.png, a PNG image of the dataset;
• niederreiter2_02_10000.txt, M = 2, N = 10000, BASE = 2, SKIP = 4096;

Datasets in M = 7 dimensions include:

• niederreiter2_07_00010.txt, M = 7, N = 10, BASE = 2, SKIP = 4096;
• niederreiter2_07_00100.txt, M = 7, N = 100, BASE = 2, SKIP = 4096;
• niederreiter2_07_01000.txt, M = 7, N = 1000, BASE = 2, SKIP = 4096;
• niederreiter2_07_10000.txt, M = 7, N = 10000, BASE = 2, SKIP = 4096;

Datasets in M = 16 dimensions include:

• niederreiter2_16_00010.txt, M = 16, N = 10, BASE = 2, SKIP = 4096;
• niederreiter2_16_00100.txt, M = 16, N = 100, BASE = 2, SKIP = 4096;
• niederreiter2_16_01000.txt, M = 16, N = 1000, BASE = 2, SKIP = 4096;
• niederreiter2_16_10000.txt, M = 16, N = 10000, BASE = 2, SKIP = 4096;

You can go up one level to the DATASETS directory.