Orthogonal arrays generalize the idea of mutually orthogonal latin squares in a tabular form.
2.
The parallel class structure of an affine plane of order may be used to construct a set of mutually orthogonal latin squares.
3.
This construction is completely reversible and so strength 2, index 1 orthogonal arrays can be constructed from sets of mutually orthogonal latin squares.
4.
The eponymous Lam's problem is equivalent to finding a finite projective plane of order 10 or finding 9 orthogonal Latin squares of order 10.
5.
It has also been proved that if the number of frequencies is a prime or a power of a prime, the orthogonal Latin squares produce error detecting codes that are as efficient as possible.
6.
A set of Latin squares of the same order forms a set of "'mutually orthogonal Latin squares ( MOLS ) "'if every pair of Latin squares in the set are orthogonal.
7.
The latin squares produced in this way from an orthogonal array will be orthogonal latin squares, so the " k " " 2 columns other than the indexing columns will produce a set of " k " " 2 mutually orthogonal latin squares.
8.
The latin squares produced in this way from an orthogonal array will be orthogonal latin squares, so the " k " " 2 columns other than the indexing columns will produce a set of " k " " 2 mutually orthogonal latin squares.
9.
He is notable for his breakthrough work along with R . C . Bose and S . S . Shrikhande in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that there do not exist two mutually orthogonal latin squares of order 4 " n " + 2 for every " n ".
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