OFFSET
0,3
COMMENTS
The mcc lattice is generated by the vectors (u,v,0), (u,0,v) and (0,v,v), where u = 2^(-1/2), v = 2^(-1/4).
The norms q = X.X of the lattice points X have the form q = s/2 + t/sqrt(2) for integers s and t.
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd. ed., 1993. p. xxiv. (Note that the second set of generators should be [0, +-v, +-v].)
LINKS
J. H. Conway and N. J. A. Sloane, On lattices equivalent to their duals, J. Number Theory 48 (1994) 373-382.
J. H. Conway and N. J. A. Sloane, The Optimal Isodual Lattice Quantizer in Three Dimensions, Advances in Math. of Commun., Vol. 1, No. 2 (2007), 257-260; arXiv:math/0701080 [math.NT], 2007.
G. Nebe and N. J. A. Sloane, Home page for mcc lattice.
Warren D. Smith, The theta series of the (det=1, isodual) MCC lattice. [Gives first 775 terms.]
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 14 2013
EXTENSIONS
a(18) onwards computed by Warren D. Smith
STATUS
approved