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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

NEW CONSTRUCTION METHOD OF RECTANGULAR PARTIALLY BALANCED INCOMPLETE BLOCK DESIGNS AND SINGULAR GROUP DIVISIBLE DESIGNS

Rezgui Imane1 and Z. Gheribi-Aoulmi1
  • 1 University Constantine 1, Algeria

Abstract

In this study, we propose a new method of construction of rectangular Partially Balanced Incomplete Block (PBIB) designs of size k = 2s and 2≤s < l and singular Group Divisible (GD) designs of size k = 2l, l is the number of columns in a rectangular matrix containing v = n × l treatments. We give the parameters expression of the obtained designs. Furthermore, we provide two algorithms of calculation for practical use.

Journal of Mathematics and Statistics
Volume 10 No. 1, 2014, 45-48

DOI: https://doi.org/10.3844/jmssp.2014.45.48

Submitted On: 13 October 2013 Published On: 9 January 2014

How to Cite: Imane, R. & Gheribi-Aoulmi, Z. (2014). NEW CONSTRUCTION METHOD OF RECTANGULAR PARTIALLY BALANCED INCOMPLETE BLOCK DESIGNS AND SINGULAR GROUP DIVISIBLE DESIGNS. Journal of Mathematics and Statistics, 10(1), 45-48. https://doi.org/10.3844/jmssp.2014.45.48

Open AccessCopyright: © 2014 Rezgui Imane and Z. Gheribi-Aoulmi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Rectangular Association Scheme
  • Group Divisible Association Scheme
  • Partially Balanced Incomplete Block Design