On the extremality of the polynomials used for obtaining the best known upper bounds for the kissing numbers

We prove that the polynomials used for obtaining the best known upper bounds for some kissing numbers (the maximum number of nonoverlapping unit spheres that can touch a unit sphere in n dimensions) are best between the polynomials of the same or lower degree. We give also some extremal polynomials we have obtained using a method proposed in 4]. The upper bounds obtained in this way are slightly better than these from 1]. However the improvements are not in the integer part for dimensionsn 18.