  This article contains a proof of the MDS conjecture for $k \leq 2p-2$. That
is, that if $S$ is a set of vectors of ${\mathbb F}_q^k$ in which every subset
of $S$ of size $k$ is a basis, where $q=p^h$, $p$ is prime and $q$ is not and
$k \leq 2p-2$, then $|S| \leq q+1$. It also contains a short proof of the same
fact for $k\leq p$, for all $q$.
