  In this work, we study the performance of Reed--Solomon codes against
adversarial insertion-deletion (insdel) errors.
  We prove that over fields of size $n^{O(k)}$ there are $[n,k]$ Reed-Solomon
codes that can decode from $n-2k+1$ insdel errors and hence attain the
half-Singleton bound. We also give a deterministic construction of such codes
over much larger fields (of size $n^{k^{O(k)}}$). Nevertheless, for $k=O(\log n
/\log\log n)$ our construction runs in polynomial time. For the special case
$k=2$, which received a lot of attention in the literature, we construct an
$[n,2]$ Reed-Solomon code over a field of size $O(n^4)$ that can decode from
$n-3$ insdel errors. Earlier constructions required an exponential field size.
Lastly, we prove that any such construction requires a field of size
$\Omega(n^3)$.
