Timeline for Dense sphere packings which are not lattice packings
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 7, 2011 at 14:41 | vote | accept | Xandi Tuni | ||
| Apr 7, 2011 at 13:16 | comment | added | Henry Cohn | By the way, not only are the best current lower bounds the same for lattices and non-lattice packings in high dimensions, but so are the upper bounds, so asymptotically we are totally unable to distinguish between these cases. Still, just about everyone believes lattices must be worse eventually. A lattice in $\mathbb{R}^n$ is determined by a quadratic number of parameters, but there are an exponential number of gaps to fill, so it's just not plausible that you can do well when $n$ is huge. (However, there's little hope of making this sort of argument rigorous.) | |
| Apr 7, 2011 at 12:22 | history | answered | Henry Cohn | CC BY-SA 2.5 |