L27 ORTHOGONAL ARRAY PDF

This construction is completely reversible and so strength 2, index 1 orthogonal arrays can be constructed from sets of mutually orthogonal latin squares. Latin squares Edit As mentioned in the previous section a latin square of order n can be thought of as a 2- n, 3, 1 orthogonal array. Actually, the orthogonal array can lead to six latin squares since any ordered pair of distinct columns can be used as the indexing columns. However, these are all isotopic and are considered equivalent.

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Actually, the orthogonal array can lead to six latin squares since any ordered pair of distinct columns can be used as the indexing columns.

However, these are all isotopic and are considered equivalent. For concreteness we shall always assume that the first two columns in their natural order are used as the indexing columns. In fact, no row, column or file the cells of a particular position in the different layers need be a permutation of the n symbols. Unlike the case with latin squares, in which there are no constraints, the indexing columns of the orthogonal array representation of a latin cube must be selected so as to form a 3- n,3,1 orthogonal array.

History Edit The concepts of latin squares and mutually orthogonal latin squares were generalized to latin cubes and hypercubes, and orthogonal latin cubes and hypercubes by Kishen The present notion of orthogonal array as a generalization of these ideas, due to C.

Rao , appears in Rao Delete the first row and take the transpose to obtain the desired orthogonal array.