High-Accuracy Semidefinite Programming Bounds for Kissing Numbers
Mittelmann, Hans D. ; Vallentin, Frank
Experiment. Math., Tome 19 (2010) no. 1, p. 174-178 / Harvested from Project Euclid
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The kissing number in $n$-dimensional Euclidean space is the maximal number of nonoverlapping unit spheres that simultaneously can touch a central unit sphere. Bachoc and Vallentin developed a method to find upper bounds for the kissing number based on semidefinite programming. This paper is a report on high-accuracy calculations of these upper bounds for $n \leq 24$. The bound for $n = 16$ implies a conjecture of Conway and Sloane: there is no $16$-dimensional periodic sphere packing with average theta series $1 + 7680q^3 + 4320q^4 + 276480q^5 + 61440q^6 + \cdots.$
Publié le : 2010-05-15
Classification:  Kissing number,  semidefinite programming,  average theta series,  extremal modular form,  11F11,  52C17,  90C10 
@article{1276784788,
     author = {Mittelmann, Hans D. and Vallentin, Frank},
     title = {High-Accuracy Semidefinite Programming Bounds for Kissing Numbers},
     journal = {Experiment. Math.},
     volume = {19},
     number = {1},
     year = {2010},
     pages = { 174-178},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1276784788}
}

Mittelmann, Hans D.; Vallentin, Frank. High-Accuracy Semidefinite Programming Bounds for Kissing Numbers. Experiment. Math., Tome 19 (2010) no. 1, pp.  174-178. http://gdmltest.u-ga.fr/item/1276784788/