High-Accuracy Semidefinite Programming Bounds for Kissing Numbers

Hans Mittelmann, Frank Vallentin
2010 Experimental Mathematics  
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 theta
more » ... s 1 + 7680q 3 + 4320q 4 + 276480q 5 + 61440q 6 + • • •
doi:10.1080/10586458.2010.10129070 fatcat:2ip7ybjnwnb4jjgrmxnvnpgboa