The hexagonal versus the square lattice

Details The hexagonal versus the square lattice The hexagonal versus the square lattice

2002-04-28

arxiv.org/abs/math/0204332v1

Math. Comp. 73 (2004), 451-473

Mathematics

Number Theory

24 pages, 6 figures, 2 tables

Scientific paper

We establish Schmutz Schaller's conjecture that the hexagonal lattice is `better' than the square lattice. Schmutz Schaller (Bulletin of the AMS 35 (1998), p. 201), motivated by considerations from hyperbolic geometry, conjectured that in dimensions 2 to 8 the best known lattice sphere packings have `maximal lengths' and goes on to write: "In dimension 2 the conjecture means in particular that the hexagonal lattice is `better' than the square lattice. More precisely, let 0

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