Numerical Algorithms Group


funded by Stiftung Rheinland-Pfalz für Innovation
Project description The Sample Package (former Discrepancy Package) project focusses on the development of small, efficient, and extensible C++ code for generating and analyzing low discrepancy nets and sequences and their randomizations.
  • Superfast implementation of digital nets in base 2. Included are
    • various radical inverses,
    • shift nets,
    • Sobol' net,
    • Niederreiter net, and
    • Niederreiter-Xing net.
  • Highly efficient implementation of randomizations:
    • digit scrambling,
    • linear scrambling, and
    • full scrambling.
  • Analysis tools are available for the computation of the
    • t-parameter,
    • star discrepancy,
    • L2 discrepancy,
    • minimum distance on unit cube and torus,
    • cap discrepancy,
    • maximum angle, and
    • minimum angle.
  • Visualization tools for LaTeX and PDFLaTeX.
Release Notes
  • Download the current version 0.5

  • The first release is extended by shift nets and more analysis tools. Besides code for the calculation of the minimum distance of a point set, also tools for spherical point sets are included like e.g. the cap discrepancy.
  • Version 0.0 provided code for the direct fast calculation of various radical inverses, digital nets (including Niederreiter-Xing) and randomized versions in base 2, and for the calculation of various discrepancies. The use of the library is demonstrated  by providing some analysis tools such as the visualization or the calculation of various discrepancies and the t-parameter of the generated nets.
Platforms The software is tested under HPUX 10.20 and Suse/Red Hat Linux. Nevertheless there should be no problems to compile the library on other platforms.
Contact Information Please feel free to report bugs, problems, and suggestions for improvements to or
© Copyrights 2002 by Thomas Kollig and Alexander Keller.

All rights reserved. You may not distribute this software, in whole or in part, especially not as part of any commercial product, without the express consent of the authors. There is no warranty or other guarantee of fitness of this software for any purpose. It is provided solely "as is".