On Lower Bounds of the Density of Delone Sets and Holes in Sequences of Sphere Packings
Muraz, G. ; Verger-Gaugry, J. -L.
Experiment. Math., Tome 14 (2005) no. 1, p. 47-57 / Harvested from Project Euclid
We study lower bounds of the packing density of a system of nonoverlapping equal spheres in $\rb^{n}, n \geq 2,$ as a function of the maximal circumradius of its Voronoi cells. Our viewpoint, using Delone sets, allows us to investigate the gap between the upper bounds of Rogers or Kabatjanskii-Levenstein and the Minkowski-Hlawka type lower bounds for the density of lattice-packings, without entering the fundamental problem of constructing Delone sets with Delone constants between $2^{-0.401}$ and $1$. As a consequence we provide explicit asymptotic lower bounds of the covering radii (holes) of the Barnes-Wall, Craig, and Mordell-Weil lattices, respectively $BW_{n},$ $\ab_{n}^{(r)},$ and $MW_{n}$, and of the Delone constants of the BCH packings, when $n$ goes to infinity.
Publié le : 2005-05-14
Classification:  Delone set,  sphere packing,  density,  hole,  52C17,  52C23
@article{1120145569,
     author = {Muraz, G. and Verger-Gaugry, J. -L.},
     title = {On Lower Bounds of the Density of Delone Sets and Holes in Sequences of Sphere Packings},
     journal = {Experiment. Math.},
     volume = {14},
     number = {1},
     year = {2005},
     pages = { 47-57},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1120145569}
}
Muraz, G.; Verger-Gaugry, J. -L. On Lower Bounds of the Density of Delone Sets and Holes in Sequences of Sphere Packings. Experiment. Math., Tome 14 (2005) no. 1, pp.  47-57. http://gdmltest.u-ga.fr/item/1120145569/