Nested Steiner \(n\)-Cycle Systems and Perpendicular Arrays

We prove that for any odd positive integer \(n > 1\) and for any sufficiently large integer \(v > v_0(n)\), there exists a Nested Steiner \(n\)-Cycle System of order \(v\) if and only if \(v \equiv 1 \pmod{2n}\). This gives rise to many new classes of perpendicular arrays.