If subset size were known, you'd be counting the combinations.

for my $n (100) {
  for my $m (1..100) {
    my $i = 1;
    $i *= ($n+1-$_)/$_ for 1..$m;
    printf "C($m,$n) = $i (%.3f bits)\n", log($i)/log(2);
  }
}
[download]

Sadly, representing even three elements requires > 16 bits.