Mutually orthogonal equitable Latin rectangles

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Let ab=n2. We define an equitable Latin rectangle as an a×b matrix on a set of n symbols where each symbol appears either bn⌉ or ⌊bn⌋ times in each row of the matrix and either an⌉ or ⌊an⌋ times in each column of the matrix. Two equitable Latin rectangles are orthogonal in the usual way. Denote a set of ka×b mutually orthogonal equitable Latin rectangles as a k MOELR (a,b;n). When a≠9,18,36, or 100, then we show that the maximum number of k MOELR (a,b;n) < 3 for all possible values of (a,b). © 2011 Elsevier B.V. All rights reserved.

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Discrete Mathematics