  For a given $n$, what is the smallest number $k$ such that every sequence of
length $n$ is determined by the multiset of all its $k$-subsequences? This is
called the $k$-deck problem for sequence reconstruction, and has been
generalized to the two-dimensional case -- reconstruction of $n\times
n$-matrices from submatrices. Previous works show that the smallest $k$ is at
most $O(n^\frac{1}{2})$ for sequences and at most $O(n^\frac{2}{3})$ for
matrices. We study this $k$-deck problem for general dimension $d$ and prove
that, the smallest $k$ is at most $O(n^\frac{d}{d+1})$ for reconstructing a $d$
dimensional hypermatrix of order $n$ from the multiset of all its
subhypermatrices of order $k$.
