Constants in the entropy number of the Sobolev space

Question

For a Sobolev space with $W^s(\Omega)$, where $\Omega\subset R^d$ is a compact space with smooth boundary, we know that the entropy number satisfies $e(\delta, W^s(\Omega, 1),\|\cdot\|_{L_\infty})\leq C(s,d)\delta^{-d/s}$, where $W^s(\Omega, 1)$ is the unit ball of the Sobolev space $W^s(\Omega)$. I am wondering if there are any upper bounds on the constant $C(s,d)$ in terms of $s$ and $d$, like $C(s,d)\leq poly(s)^d$ or something?