New Conjectural Lower Bounds on the Optimal Density of Sphere Packings
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چکیده
منابع مشابه
New Conjectural Lower Bounds on the Optimal Density of Sphere Packings
Sphere packings in high dimensions interest mathematicians and physicists and have direct applications in communications theory. Remarkably, no one has been able to provide exponential improvement on a 100-year-old lower bound on the maximal packing density due to Minkowski in d-dimensional Euclidean space R. The asymptotic behavior of this bound is controlled by 2 in high dimensions. Using an ...
متن کاملNew Provisional Lower Bounds on the Optimal Density of Sphere Packings
Sphere packings in high dimensions interest mathematicians and physicists and have direct applications in communications theory. Remarkably, no one has been able to provide exponential improvement on a 100-year-old lower bound on the maximal packing density due to Minkowski in d-dimensional Euclidean space Rd. The asymptotic behavior of this bound is controlled by 2 in high dimensions. Using an...
متن کاملNew Upper Bounds on Sphere Packings I
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
متن کاملNew Upper Bounds on Sphere Packings I
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
متن کاملNew upper bounds on sphere packings II
We continue the study of the linear programming bounds for sphere packing introduced by Cohn and Elkies. We use theta series to give another proof of the principal theorem, and present some related results and conjectures. This article is in the arXiv as: arXiv:math.MG/0110010 Dedicated to Daniel Lewin (14 May 1970 { 11 September 2001) AMS Classi cation numbers Primary: 52C17, 52C07 Secondary: ...
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ژورنال
عنوان ژورنال: Experimental Mathematics
سال: 2006
ISSN: 1058-6458,1944-950X
DOI: 10.1080/10586458.2006.10128964