  In the Bin Packing problem, given a set of items, the objective is to find a
packing of the items into the minimum number of bins possible. Vector Bin
Packing is a natural generalization of the classic bin packing problem where
given a set of $d$-dimensional vectors from $(0,1]^d$, and the aim is to
partition the set into bins such that for each bin B, we have
$\left\|\sum_{v\in B}v\right\|_\infty\leq 1$. Woeginger claimed to prove (in
[Woe97]) that the problem has no APTAS for dimensions greater than 2.
  We note that there was a slight oversight in the original proof. Hence, we
give a revised proof using some additional ideas from [BCKS06]. In fact, we
show that it is NP-hard to get an asymptotic approximation ratio better than
$\frac{600}{599}$.
