Abstract
We give a construction of p orthogonal Latin p-dimensional cubes (or Latin hypercubes) of order n for every natural number n ≠ 2, 6 and p ≥ 2. Our result generalizes the well known result about orthogonal Latin squares published in 1960 by R. C. Bose, S. S. Shikhande and E. T. Parker.
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References
R. C. Bose, S. S. Shrikhande and E. T. Parker: Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture. Canad. J. Math. 12 (1960), 189–203.
J. Denes and A. D. Keedwel: Latin Squares and Their Applications. Akademiai Kiado, Budapest, 1974.
G. L. Mullen: Orthogonal hypercubes and related designs. J. Stat. Plann. Inference 73 (1998), 177–188.
M. Trenkler: Magic p-dimensional cubes of order n ≢ 2 (mod 4). Acta Arithmetica 92 (2000), 189–194.
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Trenkler, M. On Orthogonal Latin p-Dimensional Cubes. Czech Math J 55, 725–728 (2005). https://doi.org/10.1007/s10587-005-0060-7
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DOI: https://doi.org/10.1007/s10587-005-0060-7