Definition
A t-(v,k,λ) orthogonal array (t ≤ k) is a λvt × k array whose entries are chosen from a set X with v points such that in every subset of t columns of the array, every t-tuple of points of X appears in exactly λ rows.
In this formal definition, provision is made for repetition of the t-tuples (λ is the number of repeats) and the number of rows is determined by the other parameters.
In many applications these parameters are given the following names:
- v is the number of levels,
- k is the number of factors,
- λvt is the number of experimental runs,
- t is the strength, and
- λ is the index.
An orthogonal array is simple if it does not contain any repeated rows.
An orthogonal array is linear if X is a finite field of order q, Fq (q a prime power) and the rows of the array form a subspace of the vector space (Fq)k.
Every linear orthogonal array is simple.
Read more about this topic: Hyper-Graeco-Latin Square Design
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