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Journal of Statistical Theory and Practice

, Volume 4, Issue 2, pp 203–220 | Cite as

Cyclic Polygonal Designs with Block Size 3 and λ = 1 for Joint Distance α = 6 to 16

  • M. H. Tahir
  • Ijaz Iqbal
  • Munir Akhtar
  • Javid Shabbir
Article

Abstract

Stufken (1993) first introduced cyclic polygonal designs (CPDs) (in terms of cyclic balanced sampling plans excluding adjacent units (CBSAs)) for joint distance α ≥ 2. Wei (2002) first suggested the use of Langford sequence for the existence and construction of CPDs with block size k = 3 and λ = 1 for arbitrary α. Zhang and Chang (2005b) used Langford and extended Langford sequence, and constructed CPDs (in terms of CBSAs) with block size k = 3 and λ = 1 for joint distance α = 2; 3. Zhang and Chang (2006) also constructed CPDs by using Langford sequence with k = 3 and λ = 1 for joint distance α = 4. Mandal, Parsad and Gupta (2008a) used symmetrically repeated differences and linear programming approach and gave a catalog of CPDs with k = 3, and λ = 1 for joint distance α = 2;3;4 and for some ν. In this paper, we use the method of cyclic shifts and constructed CPDs with k = 3 and λ = 1 for joint distance α = 6 to 16. A catalog of non-fractional and fractional (or smaller) CPDs for λ ≤ 100 treatments is compiled.

AMS Subject Classification

05B05 62K10 62D05 

Keywords

BIBD Cyclic BSA Cyclic block design Cyclic polygonal design Cyclic shifts Distance between the units PBIBD 

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Copyright information

© Grace Scientific Publishing 2010

Authors and Affiliations

  • M. H. Tahir
    • 1
  • Ijaz Iqbal
    • 2
  • Munir Akhtar
    • 3
  • Javid Shabbir
    • 4
  1. 1.Department of StatisticsThe Islamia University of BahawalpurBahawalpurPakistan
  2. 2.Department of StatisticsBahauddin Zakariya UniversityMultanPakistan
  3. 3.COMSATS Institute of Information and TechnologyWah CanttPakistan
  4. 4.Department of StatisticsQuaid-i-Azam UniversityIslamabadPakistan

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