Nested Steiner $n$-Cycle Systems and Perpendicular Arrays

Abstract

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 $v\equiv 1(\mathrm{mod}2n)$. This gives rise to many new classes of perpendicular arrays.