  In the $d$-dimensional hypercube bin packing problem, a given list of
$d$-dimensional hypercubes must be packed into the smallest number of hypercube
bins. Epstein and van Stee [SIAM J. Comput. 35 (2005)] showed that the
asymptotic performance ratio $\rho$ of the online bounded space variant is
$\Omega(\log d)$ and $O(d/\log d)$, and conjectured that it is $\Theta(\log
d)$. We show that $\rho$ is in fact $\Theta(d/\log d)$, using probabilistic
arguments.
