Cyclic orthogonal and balanced arrays

Abstract Kuriki and Fuji-Hara (1994) introduced an ( r , λ )-design with mutually balanced nested subdesigns (( r , λ )-design with MBN), which is equivalent to a balanced array of strength 2 with s symbols, and gave some constructions of such ( r , λ )-designs. In this paper, we consider cyclic orthogonal and balanced arrays, and we give a cyclic version of the results obtained by them. Furthermore, we give a construction of a cyclic ( r , λ )-design with MBN by a product method. By the construction, new cyclic balanced arrays with s ⩾ 3 are presented.