  We show that given any six numbers $r,s,t,u,v,w \in (0,1]$ satisfying $r \leq
s \leq \min(t,u) \leq \max(t,u) \leq v \leq w$, it is possible to construct a
compact subset of $[0,1]$ with Hausdorff dimension equal to $r$, lower modified
box dimension equal to $s$, packing dimension equal to $t$, lower box dimension
equal to $u$, upper box dimension equal to $v$ and Assouad dimension equal to
$w$. Moreover, the set constructed is an $r$-Hausdorff set and a $t$-packing
set.
