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

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 v. In this paper, we use the method of cyclic shifts and constructed CPDs with k = 3 and λ = 1 for joint distance λ = 6 to 16. A catalog of non-fractional and fractional (or smaller) CPDs for v ≤ 100 treatments is compiled.

Key Words:

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