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High-Accuracy Semidefinite Programming Bounds for Kissing Numbers
The kissing number in n-dimensional Euclidean space is the maximal number of non-overlapping unit spheres which 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 ≤ 24. The bound for n = 16 implies a conjecture of Conway and Sloane: There is no 16-dimensional periodic point set with average thetadoi:10.1080/10586458.2010.10129070 fatcat:2ip7ybjnwnb4jjgrmxnvnpgboa