The spectrum of cyclic BSA(ν, 3, λ; α) with α = 2, 3

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao, and Stufken in 1988. In this paper, we generalize the concept of a cyclic BSEC to a cyclic balanced sampling plan to avoid the selection of adjacent units (or CBSA for short) and use Langford and extended Langford sequences to construct a cyclic BSA(ν, 3, λ; α) with α = 2, 3. We finally establish the necessary and sufficient conditions for the existence of a cyclic BSA(ν, 3, λ; α) where α = 2, 3. © 2005 Wiley Periodicals, Inc. J Combin Designs.