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
Famous quotes containing the word definition:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)