  For codes equipped with metrics such as Hamming metric, symbol pair metric or
cover metric, the Johnson bound guarantees list-decodability of such codes.
That is, the Johnson bound provides a lower bound on the list-decoding radius
of a code in terms of its relative minimum distance $\delta$, list size $L$ and
the alphabet size $q.$ For study of list-decodability of codes with insertion
and deletion errors (we call such codes insdel codes), it is natural to ask the
open problem whether there is also a Johnson-type bound. The problem was first
investigated by Wachter-Zeh and the result was amended by Hayashi and Yasunaga
where a lower bound on the list-decodability for insdel codes was derived.
  The main purpose of this paper is to move a step further towards solving the
above open problem. In this work, we provide a new lower bound for the
list-decodability of an insdel code. As a consequence, we show that unlike the
Johnson bound for codes under other metrics that is tight, the bound on
list-decodability of insdel codes given by Hayashi and Yasunaga is not tight.
Our main idea is to show that if an insdel code with a given Levenshtein
distance $d$ is not list-decodable with list size $L$, then the list decoding
radius is lower bounded by a bound involving $L$ and $d$. In other words, if
the list decoding radius is less than this lower bound, the code must be
list-decodable with list size $L$. At the end of the paper we use such bound to
provide an insdel-list-decodability bound for various well-known codes, which
has not been extensively studied before.
