Abstract
In general it is a difficult if not impossible task to find a latin square orthogonal to a given latin square. Because of a practical problem it was required to find a frequency square orthogonal to a given latin square. We describe a computer approach which was successful in finding a (4,23) frequency square orthogonal to a given 10×10 latin square.
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References
Walter T. Federer, "On the existence and construction of a complete set of orthogonal F(4t;2t,2t)-squares", Paper No. BU-564-M in the Biometrics Unit Mimeo Series, Department of Plant Breeding and Biometry, Cornell University, Ithaca, New York, 1975.
A. Hedayat, On the Theory of the Existence, Non-existence and the Construction of Mutually Orthogonal F-squares and Latin Squares, Ph.D. Dissertation, Cornell University, 1969.
A. Hedayat and E. Seiden, "F-square and orthogonal F-squares design: generation of latin square and orthogonal latin squares design", Ann. Math. Statistics 41 (1970), 2035–2044.
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© 1978 Springer-Verlag
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Kirton, H.C., Seberry, J. (1978). Generation of a frequency square orthogonal to a 10×10 latin square. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062532
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DOI: https://doi.org/10.1007/BFb0062532
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08953-7
Online ISBN: 978-3-540-35702-5
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