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Encyclopaedia of DesignTheory: MOLS

General Partition Incidence Array

Experimental Other designs Math properties Stat properties

Server External Bibliography Miscellaneous

Mutually orthogonal Latin squares

The number of mutually orthogonal Latin squares of order n is at most n-1.

If q is a prime power, there exist q-1 MOLS of order q. These are constructed by the "finite field method". For there exists a Galois field F of order q. Now, for each non-zero element a od F, let L_a be the array, with rows and columns indexed by F, such that the symbol in row x and column y of L_a is ax+y. Then the arrays L_a form the required q-1 MOLS.

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Peter J. Cameron
16 April 2002

General	Partition	Incidence	Array
Experimental	Other designs	Math properties	Stat properties
Server	External	Bibliography	Miscellaneous