

A211215


Total number of Latin ndimensional hypercubes of order 4; labeled nary quasigroups of order 4.


1



4, 24, 576, 55296, 36972288, 6268637952000, 80686060158523011084288, 4465185218736554544676917926460256725000192, 4558271384916189349044295395852008182480786230841798008741684281906576963885826048
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OFFSET

0,1


COMMENTS

The values are calculated recursively, based on the characterization by 2009. The number a(5) was found before (2001 and, independently, later works) by exhaustive computeraided classification of the objects.


REFERENCES

D. S. Krotov, V. N. Potapov, On the reconstruction of Nquasigroups of order 4 and the upper bounds on their numbers, Proc. Conference devoted to the 90th anniversary of Alexei A. Lyapunov (Novosibirsk, Russia, October 811, 2001), 2001, http://www.ict.nsc.ru/ws/Lyap2001/2363/
T. Ito, Creation Method of Table, Creation Apparatus, Creation Program and Program Storage Medium, U.S. Patent application 20040243621, Dec 02 2004
B. D. McKay, I. M. Wanless, A census of small latin hypercubes, SIAM J. Discrete Math. 22:2 (2008) 719736


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KEYWORD

nonn


AUTHOR

Denis S. Krotov and Vladimir N. Potapov, Apr 06 2012


STATUS

approved



