  Permutation codes in the Ulam metric, which can correct multiple deletions,
have been investigated extensively recently owing to their applications. In
this work, we are interested in the maximum size of the permutation codes in
the Ulam metric and aim to design permutation codes that can correct multiple
deletions with efficient decoding algorithms. We first present an improvement
on the Gilbert--Varshamov bound of the maximum size of these permutation codes
which is the best-known lower bound. Next, we focus on designing permutation
codes in the Ulam metric with a decoding algorithm. These constructed codes are
the best-known permutation codes that can correct multiple deletions. In
particular, the constructed permutation codes can correct $t$ deletions with at
most $(3t-1) \log n+o(\log n)$ bits of redundancy where $n$ is the length of
the code. Finally, we provide an efficient decoding algorithm for our
constructed permutation codes.
