Direct Constructions for General Families of Cyclic Mutually Nearly Orthogonal Latin Squares |
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Authors: | Fatih Demirkale Diane Donovan Abdollah Khodkar |
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Affiliation: | 1. Department of Mathematics, Ko? University, Turkey;2. Department of Mathematics, The University of Queensland, Brisbane, QLD, Australia;3. Department of Mathematics, University of West Georgia, Carrollton, USA |
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Abstract: | Two Latin squares and , of even order n with entries , are said to be nearly orthogonal if the superimposition of L on M yields an array in which each ordered pair , and , occurs at least once and the ordered pair occurs exactly twice. In this paper, we present direct constructions for the existence of general families of three cyclic mutually orthogonal Latin squares of orders , , and . The techniques employed are based on the principle of Methods of Differences and so we also establish infinite classes of “quasi‐difference” sets for these orders. |
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Keywords: | Latin squares nearly orthogonal Latin squares orthogonal Latin squares quasi‐difference sets |
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