Assuming you're doing a numerical comparison on the first part of the filename, you want code rather more like this:

my ($greatest, $gnum) = ('', 0);
while($file = readdir DIR) {
    (my $fnum = $file) =~ /^(\d+)\./;
    next unless $fnum > $gnum;
    $gnum = $fnum;
    $greatest = $file;
}
[download]

There's room for more polish, but the general idea is there.