The spectrum of cyclic BSEC with block size three

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this paper, we discuss these designs having cyclic automorphisms. We use Langford sequence to construct all admissible cyclic BSEC (or CBSEC) of block size 3. As consequent we obtain that the existence spectrum of a CBSEC(v,3,λ) are either v∈{1,3}, or v⩾9 and λ(v-3)≡0(mod6) but v≢2(mod4) when λ≡2(mod4).