  We focus on classical and quantum list decoding. The capacity of list
decoding was obtained by Nishimura in the case when the number of list does not
increase exponentially. However, the capacity of the exponential-list case is
open even in the classical case while its converse part was obtained by
Nishimura. We derive the channel capacities in the classical and quantum case
with an exponentially increasing list. The converse part of the quantum case is
obtained by modifying Nagaoka's simple proof for strong converse theorem for
channel capacity. The direct part is derived by a quite simple argument.
