OFFSET
1,1
COMMENTS
It is known that a(12) through a(24) are at least 1, 0, 1, 0, 3, 0, 1, 0, 1, 1, 5, 4, 2 respectively.
In this sequence, the dual pairs of lattices are counted as one if they are both strongly perfect (it is not always so). E.g., in dimensions 6, 7, 10 there are two strongly perfect lattices, forming a dual pair, but in dimension 21 there is a strongly perfect lattice which has a not strongly perfect dual. - Andrey Zabolotskiy, Feb 20 2021
REFERENCES
J. Martinet, Les réseaux parfaits des espaces euclidiens, Masson, Paris, 1996.
J. Martinet, Perfect Lattices in Euclidean Spaces, Springer-Verlag, NY, 2003. See Section 16.2.
LINKS
B. Venkov, Réseaux et designs sphériques, pp. 10-86 in Réseaux Euclidiens, Designs Sphériques et Formes Modulaires, ed. J. Martinet, L'Enseignement Mathématique, Geneva, 2001.
Jacques Martinet, Known strongly perfect lattices, 2002-2020.
CROSSREFS
KEYWORD
nonn,nice,hard,more
AUTHOR
N. J. A. Sloane, Nov 16 2001
STATUS
approved