Cyclic BSEC of block size 3

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this note, we discuss constructions of these designs having cyclic automorphisms. We use Langford sequences to construct all possible cyclic BSEC (or CBSEC) with block size 3 and λ = 1,2, which establishes the necessary and sufficient conditions for such designs. Some constructions of the balanced sampling plan avoiding adjacent units, a generalization of BSEC, are also given for fixed λ.