  A collection $\mathcal S$ of equivalence classes of positive definite
integral quadratic forms in $n$ variables is called an $n$-exceptional set if
there exists a positive definite integral quadratic form which represents all
equivalence classes of positive definite integral quadratic forms in $n$
variables except those in $\mathcal S$. We show that, among other results, for
any given positive integers $m$ and $n$, there is always an $n$-exceptional set
of size $m$ and there are only finitely many of them.
