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Number of strongly eutactic lattices in dimension n.
4

%I #13 Feb 22 2021 07:45:42

%S 1,2,3,6,9,21

%N Number of strongly eutactic lattices in dimension n.

%D J. Martinet, Les reseaux parfaits des espaces Euclidiens, Masson, Paris, 1996.

%D J. Martinet, Perfect Lattices in Euclidean Spaces, Springer-Verlag, NY, 2003.

%D G. Nebe, Review of J. Martinet, Perfect Lattices in Euclidean Spaces, Bull. Amer. Math. Soc., 41 (No. 4, 2004), 529-533.

%H Christian Batut and Jacques Martinet, <a href="http://jamartin.perso.math.cnrs.fr/Lattices/webdesign.pdf">Lattices and spherical designs</a>, 2005-2014. See pages 12-13.

%H J. Martinet and B. Venkov, <a href="https://jamartin.perso.math.cnrs.fr/Publications/fOrteutensmath.pdf">Les réseaux fortement eutactiques</a>, pp. 112-132 in Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, ed. J. Martinet, L'Enseignement Mathématique, Geneva, 2001.

%Y Cf. A037075, A065535, A004026.

%K nonn,nice,hard,more

%O 1,2

%A _N. J. A. Sloane_, Nov 16 2001

%E It is known that a(6) >= 19, a(7) >= 10.

%E a(5) corrected and a(6) added from Batut & Martinet by _Andrey Zabolotskiy_, Feb 20 2021