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 v. 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 v≤ 100 treatments is compiled. AMS Subject Classification: 05B05; 62K10; 62D05. Key-words: BIBD; Cyclic BSA; Cyclic block design; Cyclic polygonal design; Cyclic shifts; Distance between the units; PBIBD.