Designs, Codes and Cryptography

, Volume 67, Issue 2, pp 233–243 | Cite as

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 kt > 1 are also presented.


Orthogonal arrays t-Quasigroups Nested orthogonal arrays Existence 

Mathematics Subject Classification (2000)

05B15 62K15 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsSoochow UniversitySuzhouChina

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