Huffman Redundancy for Large Alphabet Sources

The performance of optimal prefix-free encoding for memoryless sources with a large alphabet size is studied. It is shown that the redundancy of the Huffman code for almost all sources with a large alphabet size
$n$
is very close to that of the average distribution of the monotone sources with
$n$
symbols. This value lies between 0.02873 and 0.02877 bit for sufficiently large
$n$
.