High-Accuracy Semidefinite Programming Bounds for Kissing Numbers
نویسندگان
چکیده
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 + 7680q + 4320q + 276480q + 61440q + · · ·
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ورودعنوان ژورنال:
- Experimental Mathematics
دوره 19 شماره
صفحات -
تاریخ انتشار 2010