Projective properties of certain orthogonal arrays
نویسندگان
چکیده
منابع مشابه
Projection properties of certain three level orthogonal arrays
Two orthogonal arrays based on 3 symbols are said to be isomorphic or combinatorially equivalent if one can be obtained from the other by a sequence of row permutations, column permutations and permutations of symbols in each column. Orthogonal arrays are used as screening designs to identify active main effects, after which the properties of the subdesign for estimating these effects and possi...
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We prove that binary orthogonal arrays of strength 8, length 12 and cardinality 1536 do not exist. This implies the nonexistence of arrays of parameters (strength,length,cardinality) = (n, n + 4, 6.2) for every integer n ≥ 8.
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We consider orthogonal arrays of strength two and even order q having n columns which are equivalent to n − 2 mutually orthogonal Latin squares of order q. We show that such structures induce graphs on n vertices, invariant up to complementation. Previous methods worked only for single Latin squares of even order and were harder to apply. If q is divisible by four the invariant graph is simple ...
متن کاملOrthogonal Arrays
Definition Orthogonal arrays (OAs) are objects that are most often generated via algebraic arguments. They have a number of applications in applied mathematics, and have often been studied by algebraic mathematicians as objects of interest in their own right. Our treatment will reflect their use as representations of statistical experimental designs. An OA is generally presented as a two-dimens...
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(say) is called symmetric, otherwise, the array is said to be asymmetric. Several methods of construction of symmetric as well as asymmetric OAs are available in the literature. Some important methods will be discussed here. One of the principal applications of the OAs is in the selection of level combinations for fractional factorial experiments. An OA of strength t is equivalent to an orthogo...
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ژورنال
عنوان ژورنال: Biometrika
سال: 1996
ISSN: 0006-3444,1464-3510
DOI: 10.1093/biomet/83.4.950