Geodesic
$ k$-homogeneous Latin Squares, their transversals and condition of orthogonality
Matematičeskie voprosy kriptografii, Tome 13 (2022) no. 3, pp. 45-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the $k$-homogeneous Latin Squares, i.e. Latin Squares of order $kn$ with elements from $\{0,\dots,kn-1\}$ such that reducing modulo $n$ gives $(kn \times kn)$-matrix consisting of $k^2$ identical Latin Squares of order $n$. Some characteristics of transversals for $k$-homogeneous Latin Squares are described. Sufficient condition of orthogonality is presented. 
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V. V. Borisenko. $ k$-homogeneous Latin Squares, their transversals and condition of orthogonality. Matematičeskie voprosy kriptografii, Tome 13 (2022) no. 3, pp. 45-54. http://geodesic.mathdoc.fr/item/MVK_2022_13_3_a2/

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