  The $n$-grid $E_n$ consists of $n$ equally spaced points in $[-1,1]$
including the endpoints $\pm 1$. The extremal polynomial $p_n^*$ is the
polynomial that maximizes the uniform norm $\| p \|_{[-1,1]}$ among polynomials
$p$ of degree $\leq \alpha n$ that are bounded by one on $E_n$. For every
$\alpha \in (0,1)$, we determine the limit of $\frac{1}{n} \log \|
p_n^*\|_{[-1,1]}$ as $n \to \infty$. The interest in this limit comes from a
connection with an impossibility theorem on stable approximation on the
$n$-grid.
