In this talk we will discuss Tammes', kissing number and several other sphere packings problems in dimensions three and four. I will consider various approaches to solving these problems and in particular solution methods related to distance graphs. I present an extension of known semidefinite and linear programming upper bounds for spherical codes. The main result can be applied for the distance distribution of a spherical code, and it will be shown that this method can work effectively. In particular, I get a shorter solution to the kissing number problem in dimension 4.