NEW UPPER BOUNDS FOR KISSING NUMBERS FROM SEMIDEFINITE PROGRAMMING

摘要

To complete the picture, let us discuss uniqueness of the optimal point configurations.For dimensions 8 and 24, uniqueness was proved by E. Bannai and N.J.A. Sloane ([3]). Their proof exploits the fact that the LP method obtains exactly the aimed value. For dimension 3, there are infinitely many possible configurations.In the regular icosahedron configuration, the angular distances between he contact points are strictly greater than the required i/3; hence these points cyan be moved around obtaining infinitely many new suitable configurations.