Abstract
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.
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Wang, K., Yin, J. Further results on the existence of nested orthogonal arrays. Des. Codes Cryptogr. 67, 233–243 (2013). https://doi.org/10.1007/s10623-011-9603-0
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DOI: https://doi.org/10.1007/s10623-011-9603-0