On the number of latin hypercubes, pairs of orthogonal latin squares and MDS codes

Vladimir N. Potapov

Published 2015-10-21Version 1

The logarithm of the number of latin $d$-cubes of order $n$ is $\Theta(n^d\ln n)$. The logarithm of the number of pairs of orthogonal latin squares of order $n$ is $\Theta(n^2\ln n)$. Similar estimations are obtained for systems of mutually strong orthogonal latin $d$-cubes.