Hold'em Poker Puzzle (hand with most outs)

[chapstick]

Here's a puzzle (you might only find interetsing if you're bored). I haven't though too much about it, and this might be completely trivial, but work is not so interesting right now...

Which pocket cards and set of community cards to 4th street (i.e. only the river to come) give you the most outs to the absolute nuts? The only condition, to make this non-trivial, is that on 4th street you can't have a hand better than three-of-a-kind.

For example, if you have A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/heart.gif[/img] in the pocket with A[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 9[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/diamond.gif[/img] on the board, the remaining fives in the deck are not strictly outs to the absolute nuts since villain may be holding pocket fives, and will make a four-of-a-kind. But the Queens are outs since they cant make anyone a better hand.