Perfect packing of $d$-cubes

A packing of $d$-cubes into a $d$-box of the right area is called perfect packing. Since $\sum\limits_{i =1}^\infty {1/ i^{dt}}={\zeta(dt)}$, it can be asked for which $t$ can be found a perfect packing of the $d$-cubes of edge lengths $1$, $2^{-t}$, $3^{-t}$, $\ldots$ into a $d$-box of the right area. In this paper an algorithm will be presented which packs the $d$-cubes of edge lengths $1$, $2^{-t}$, $3^{-t}$, $\ldots$ into a $d$-box of area $\zeta(dt)$ for any $t$ on the interval $[d_0,{2^{d-1}/( d2^{d-1}-1)}]$, where $d_0$ depends on $d$ only.