Before revision: }}  that Floor-ReLU networks with width \max\{d,\, 5N+13\} and depth 64dL+3 can pointwise approximate a Lipschitz continuous } function f on [0,1]^d with an exponential approximation rate 3 \mu\sqrt{d\,N}  ^{-  \sqrt{L}}, where \mu is the Lipschitz constantof f. {  More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f(\sqrt{d}\,N^{-\sqrt{L}})+2\omega_f(\sqrt{d}){N^{-\sqrt{L}}}.
After revision: }} it is shown that Floor-ReLU networks with width \max\{d,\, 5N+13\} and depth 64dL+3 can pointwise approximate a Lipschitz continuous } function f on [0,1]^d with an exponential approximation rate 3 \mu\sqrt{d\,N} ^{- \sqrt{L}}, where \mu is the Lipschitz constantof f. { More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f(\sqrt{d}\,N^{-\sqrt{L}})+2\omega_f(\sqrt{d}){N^{-\sqrt{L}}}.