IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i3d10.1007_s00362-018-0987-z.html
   My bibliography  Save this article

New lower bounds of four-level and two-level designs via two transformations

Author

Listed:
  • Hongyi Li

    (Jishou University
    Central China Normal University)

  • Hong Qin

    (Central China Normal University)

Abstract

Code theory is widely used to construct optimal designs in recent years. In this paper, two transformations, a modified Gray map and a mapping between quaternary codes and the sequence of three binary codes for four-level designs, are considered. Via the two transformations, we point out that the wrap-around $$L_2$$L2-discrepancy values of the two-level designs corresponding to a four-level design are decided by the four-level design, two new analytical expressions of the wrap-around $$L_2$$L2-discrepancy for the derived two-level designs are built, and some new lower bounds of the wrap-around $$L_2$$L2-discrepancy for four-level and two-level designs are obtained, which can be used as a benchmark for search the uniform designs and evaluate the uniformity of designs. Furthermore, based on the second transformation, we provide a very strong link between the aberration of a four-level design and the uniformity of the derived two-level design.

Suggested Citation

  • Hongyi Li & Hong Qin, 2020. "New lower bounds of four-level and two-level designs via two transformations," Statistical Papers, Springer, vol. 61(3), pages 1231-1243, June.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0987-z
    DOI: 10.1007/s00362-018-0987-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-018-0987-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-018-0987-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0987-z. 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.