On the complexity of implementation of characteristic functions of the spheres by circuits of functional elements

For characteristic functions of spheres, an asymptotics for the complexity of their implementation by circuits of functional elements in the basis $\{\&,\vee,-\}$ is established; the characteristic function of a sphere with the center at the vertex $\tilde\sigma=(\sigma_1,\ldots,\sigma_n)$, $\sigma_1,\ldots,\sigma_n\in\{0,1\}$, is the Boolean function equal to one on all those and only those sets of values of variables each of which differs from the vertex $\tilde\sigma$ only in one digit.