NIEDERREITER2
Niederreiter Quasirandom Datasets
Base = 2
NIEDERREITER2
is a dataset directory which
contains points generated
by the Mdimensional 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;
The values of M and N are specified in the dataset file names.
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:

Paul Bratley, Bennett Fox, Harald Niederreiter,
Algorithm 738:
Programs to Generate Niederreiter's LowDiscrepancy Sequences,
ACM Transactions on Mathematical Software,
Volume 20, Number 4, pages 494495, 1994.

Harald Niederreiter,
Lowdiscrepancy and lowdispersion sequences,
Journal of Number Theory,
Volume 30, 1988, pages 5170.
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.
Last revised on 31 August 2005.