As JustSid told you, it's not ANet that limits you to a max. player number but how you use the functions and possibilities ANet gives you. If you send the positions of all 16 players every frame, it won't work over internet. Not because ANet is crap, but because the internet connections can't handle the high traffic. ANet produces as less traffic as possible. It only adds data for identifying variables, addressing the receivers,... and such stuff. The traffic consumption of each function is documented in the manual and you can decide for yourself which function is best suited for your case.
There are already games like Survive!, a Goldeneye remake, CSIS,... that work great with a high number of players. You can use the "AUM76 to ANet" sample also with a higher number of players to make your own tests. Just increase the player limit in this line:
(file: main.h)
line 5: #define max_players 4 //<-- replace it with 16
I will start converting the example now, maybe I can finish it today. I will pm you when I'm done.