Abstract
Difference schemes (Bose and Bush, Ann. Math. Statist. 23 (1952), 508–524) form a useful tool for the construction of orthogonal arrays of strength 2. We study a generalization of these schemes, difference schemes of strength t, which are useful for the construction and representation of orthogonal arrays of strength t. We study the existence of difference schemes of strength t, methods for their construction, and methods to construct orthogonal arrays of strength t from these schemes.
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