  In this paper it is shown that $C_\beta$-smooth functions can be approximated
by deep neural networks with ReLU activation function and with parameters
$\{0,\pm \frac{1}{2}, \pm 1, 2\}$. The $l_0$ and $l_1$ parameter norms of
considered networks are thus equivalent. The depth, width and the number of
active parameters of the constructed networks have, up to a logarithmic 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 the constructed networks attains the same convergence rate as
with sparse networks with parameters in $[-1,1]$.
