On the number of SQSs, latin hypercubes and MDS codes∗
نویسنده
چکیده
It is established that the logarithm of the number of latin d-cubes of order n is Θ(n ln n) and the logarithm of the number of pairs of orthogonal latin squares of order n is Θ(n ln n). Similar estimations are obtained for systems of mutually strong orthogonal latin d-cubes. As a consequence, it is constructed a set of Steiner quadruple systems of order n such that the logarithm of its cardinality is Θ(n ln n) as n →∞ and n mod 6 = 2 or 4.
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تاریخ انتشار 2017