Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8

Details Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8 Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8

2004-05-23

arxiv.org/abs/math/0405441v4

International Mathematics Research Notices 32 (2005), 1937-1955

Mathematics

Metric Geometry

13 pages; (v2) major revision: proof of rigidity corrected, full discussion of E8-case included, src of (v3) contains MAGMA pr

Scientific paper

10.1155/IMRN.2005.1937

We show that the Leech lattice gives a sphere covering which is locally least dense among lattice coverings. We show that a similar result is false for the root lattice E8. For this we construct a less dense covering lattice whose Delone subdivision has a common refinement with the Delone subdivision of E8. The new lattice yields a sphere covering which is more than 12% less dense than the formerly best known given by the lattice A8*. Currently, the Leech lattice is the first and only known example of a locally optimal lattice covering having a non-simplicial Delone subdivision. We hereby in particular answer a question of Dickson posed in 1968. By showing that the Leech lattice is rigid our answer is even strongest possible in a sense.

Affiliated with

Also associated with

No associations

Rating

Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-186358