Asymptotically sharp dimension estimates for $k$-porous sets - Järvenpää, E.; Järvenpää, M.; Käenmäki, A.; Suomala, V. (Mathematica Scandinavica, 2005)
In ${\mathsf R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimension of $k$-porous sets having holes of certain size near every point in $k$ orthogonal directions at all small scales. This bound tends to $n-k$ as $k$-porosity tends to its maximum value.