IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-540-74496-2_19.html
   My bibliography  Save this book chapter

Improvements on Low Discrepancy One-Dimensional Sequences and Two-Dimensional Point Sets

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

Author

Listed:
  • Henri Faure

    (UMR 6206 CNRS, Institut de Mathématiques de Luminy)

Abstract

Summary We obtain significant improvements for the star discrepancy D* of generalized van der Corput sequences by means of linear digit scramblings (see Section 5.2 for the definition). We also find a new lower bound for the extreme discrepancy D of these sequences which permits to show that linearly-scrambled sequences are set in a good place among generalized van der Corput sequences. Finally, we derive the corresponding properties for generalized Hammersley point sets in arbitrary bases and link recent developments in base 2 by Kritzer, Larcher and Pillichshammer to former studies of Béjian and the author.

Suggested Citation

  • Henri Faure, 2008. "Improvements on Low Discrepancy One-Dimensional Sequences and Two-Dimensional Point Sets," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 327-341, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_19
    DOI: 10.1007/978-3-540-74496-2_19
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-540-74496-2_19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.