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Mutually orthogonal equitable Latin rectangles
Authors:John Asplund  Melissa S Keranen
Institution:aDepartment of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931-0402, USA
Abstract: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 View the MathML source or View the MathML source times in each row of the matrix and either View the MathML source or View the MathML source 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).
Keywords:Mutually orthogonal Latin square  Latin rectangle  Orthogonal array
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