Metric Entropy of Cartesian Product of Shrinking Intervals

Question

The metric entropy (covering number) of the unit ball in $\mathbf{R}^d$ is well known result ($\sim \epsilon^{-d}$) using the volume formula. I'm wondering if there is any result on the metric entropy of a Cartesian product of shrinking intervals of the form $\Pi_{j=1}^J[-Aj^{-k}, Aj^{-k}]$ for some constant $A>0$ and $k>\frac{1}{2}$?