High-Accuracy Semidefinite Programming Bounds for Kissing Numbers

Abstract. 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 sphere packing with average theta series 1 + 7680q3 + 4320q4 + 276480q5 + 61440q6 +

• Type: Journal
• Year: 2010
• Where: EM
• Authors: Hans D. Mittelmann, Frank Vallentin
• Keywords: EM 2010, Kissing Number, Management, N-dimensional Euclidean Space, Upper Bounds