Further results on the existence of nested orthogonal arrays

Nested orthogonal arrays provide an option for designing an experimental setup consisting of two experiments, the expensive one of higher accuracy being nested in a larger and relatively less expensive one of lower accuracy. We denote by OA_(λ, μ)(t, k, (v, w)) (or OA(t, k, (v, w)) if λ = μ = 1) a (symmetric) orthogonal array OA _λ (t, k, v) with a nested OA _μ (t, k, w) (as a subarray). It is proved in this article that an OA(t, t + 1,(v, w)) exists if and only if v ≥ 2w for any positive integers v, w and any strength t ≥ 2. Some constructions of OA_(λ, μ)(t, k, (v, w))′s with λ ≠ μ and k ? t > 1 are also presented.