Let $\{B^{(\alpha)}(t)\}_{t\in\mathbb{R}^{d}}$ be the Fractional
Brownian Sheet with multi-index $\alpha=(\alpha_1,\ldots,
\alpha_d)$, $0< \alpha_i< 1$. In \cite{Kamont1996}, Kamont has shown that,
with probability $1$, the box dimension of the graph of a
trajectory of this Gaussian field, over a non-degenerate cube
$Q\subset\mathbb{R}^{d}$ is equal to
$d+1-\min(\alpha_1,\ldots,\alpha_d)$. In this paper, we prove that
this result remains true when the box dimension is replaced by the
Hausdorff dimension or the packing dimension.