Cyclic Polygonal Designs with Block Size 3 and λ = 1 for Joint Distance α = 6 to 16
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 Classification05B05 62K10 62D05
KeywordsBIBD Cyclic BSA Cyclic block design Cyclic polygonal design Cyclic shifts Distance between the units PBIBD
Unable to display preview. Download preview PDF.
- Hedayat, A.S., Rao, C.R., Stufken, J., 1988b. Designs in survey sampling avoiding contiguous units. In Handbook of Statistics 6: Sampling, Krishnaiah P.R. and Rao C.R. (Editors), Elsevier, Amsterdam, pp. 575–583.Google Scholar
- Iqbal, I., 1991. Construction of Experimental Designs Using Cyclic Shifts. Ph.D. thesis, University of Kent at Canterbury, UK.Google Scholar
- Mandal, B.N., Parsad, R., Gupta, V.K., 2008a. Computer-aided construction of balanced sampling plans excluding contiguous units. Journal of Statistics and Applications, 3, 67–93.Google Scholar
- Tahir, M.H., Iqbal, I., Akhtar, M., Shabbir, J., 2009. Cyclic polygonal designs with block size 3 and λ = 1 for joint distance α = 2,3,4,5. Under Review in Science in China Series A: Mathematics.Google Scholar