Partitionable sets and cyclic BSECs with block size four

In this article, we introduce a combinatorial structure called a partitionable set. We use these sets to construct cyclic balanced sampling plans excluding contiguous units. Two recursive constructions for CBSEC ( v , 4 , 1 ) ʹs are established by utilizing partitionable sets and difference matrices. As consequent we get the existence of a CBSEC ( au , 4 , 1 ) where u is a product of numbers in Q = { p : p ≡ 1 ( mod 4 ) and p is prime } ∪ { q : q ≡ 1 , 5 ( mod 12 ) , q ⩽ 160 } and a ∈ { 3 , 27 , 63 , 99 , 171 , 207 , 243 } .