  In this paper it is shown that $C_\beta$-smooth functions can be approximated
by neural networks with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$. The
depth, width and the number of active parameters of constructed networks have,
up to a logarithimc factor, the same dependence on the approximation error as
the networks with parameters in $[-1,1]$. In particular, this means that the
nonparametric regression estimation with constructed networks attain the same
convergence rate as with the sparse networks with parameters in $[-1,1]$.
