Abstract
In this paper, generalized Latin matrix and orthogonal generalized Latin matrices are proposed. By using the property of orthogonal array, some methods for checking orthogonal generalized Latin matrices are presented. We study the relation between orthogonal array and orthogonal generalized Latin matrices and obtain some useful theorems for their construction. An example is given to illustrate applications of main theorems and a new class of mixed orthogonal arrays are obtained.
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The authors sincerely thank the referees for their many valuable comments which help us improving the paper.
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Supported by the National Natural Science Foundation of China (Nos. 11571094 and 11171093).
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Pang, Sq., Chen, Ly. Generalized latin matrix and construction of orthogonal arrays. Acta Math. Appl. Sin. Engl. Ser. 33, 1083–1092 (2017). https://doi.org/10.1007/s10255-017-0720-z
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DOI: https://doi.org/10.1007/s10255-017-0720-z
Keywords
- orthogonal array
- generalized Latin matrix
- orthogonal generalized Latin matrices
- matrix image
- generalized permutation difference matrix