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A Census of Small Latin Hypercubes

McKay, Brendan; Wanless, Ian

Description

We count all latin cubes of order n < 6 and latin hypercubes of order n < 5 and dimension d < 5. We classify these (hyper)cubes into isotopy classes and paratopy classes (main classes). For the same values of n and d we classify all d-ary quasigroups of order n into isomorphism classes and also count them according to the number of identity elements they possess (meaning we have counted the d-ary loops). We also give an exact formula for the number of (isomorphism classes of) d-ary quasigroups...[Show more]

CollectionsANU Research Publications
Date published: 2008
Type: Journal article
URI: http://hdl.handle.net/1885/39594
Source: SIAM Journal on Discrete Mathematics
DOI: 10.1137/070693874

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