  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 series 1 + 7680q^3 + 4320q^4 + 276480q^5
+ 61440q^6 + ...
