On the number of SQSs, latin hypercubes and MDS codes

On the number of SQSs, latin hypercubes and MDS codes We establish that the logarithm of the number of latin d‐cubes of order n is Θ(ndlnn) and the logarithm of the number of sets of t (t≥2 is fixed) orthogonal latin squares of order n is Θ(n2lnn). Similar estimations are obtained for systems of mutually strongly orthogonal latin d‐cubes. As a consequence, we construct a set of Steiner quadruple systems of order n such that the logarithm of its cardinality is Θ(n3lnn) as n→∞ and n mod 6=2 or 4. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Combinatorial Designs Wiley

On the number of SQSs, latin hypercubes and MDS codes

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Publisher
Wiley
Copyright
Copyright © 2018 Wiley Periodicals, Inc.
ISSN
1063-8539
eISSN
1520-6610
D.O.I.
10.1002/jcd.21603
Publisher site
See Article on Publisher Site

Abstract

We establish that the logarithm of the number of latin d‐cubes of order n is Θ(ndlnn) and the logarithm of the number of sets of t (t≥2 is fixed) orthogonal latin squares of order n is Θ(n2lnn). Similar estimations are obtained for systems of mutually strongly orthogonal latin d‐cubes. As a consequence, we construct a set of Steiner quadruple systems of order n such that the logarithm of its cardinality is Θ(n3lnn) as n→∞ and n mod 6=2 or 4.

Journal

Journal of Combinatorial DesignsWiley

Published: Jan 1, 2018

Keywords: ; ; ; ; ; ; ; ;

References

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