A note on perfect packing of $d$-dimensional cubes

The $d$-dimensional cubes of edges of length $\ 1, 2^{-t}, 3^{-t}, 4^{-t},\ldots $ can be packed perfectly into a $d$-dimensional box, provided $\ 1/d < t \le 2^{d-1}/(d2^{d-1}-1)$.