Existence of Five MOLS of Orders 18 and 60

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Abstract

In this article, we provide direct constructions for five mutually orthogonal Latin squares (MOLS) of orders math formula and 60. For math formula, these come from a new (60, 6, 1) difference matrix. For math formula, the required construction is obtained by combining two different methods that were used in the constructions of four MOLS(14) and eight MOLS(36).

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