Set with different fractal dimensions

Given $0<s<u<v<1$ and $s<t<v$, one can construct a Cantor set $E\subset [0,1]$ such that $\dim_H E=s, \dim_P E=t, \underline{\dim}_B E=u$ and $\overline{\dim}_B E=v$, see Sets with different dimensions in $[0,1]$,Real Analysis Exchange   by Donald W. Spear. 

Using this result, Olsen showed that for any pair of continuous functions $f,g:R^d\to [0,d]$ with $f\le g,$ it is possible to chhose a set $E$ that simultaneously has $f$ as its local Hausdorff dimension function and $g$ as its local packing dimension function. See, On simultaneous local dimension functions of subsets of $R^d$, Bull. Korean Math. Soc.