Many people don’t appreciate how a snap works.
It is not about the fingers.
A snap is your middle finger hitting the fat part of your palm. The actual snapping motion is just a way to pre-load tension on your finger and releasing it quickly.
In my technique I use my ring finger to pull down on the skin on my hand to create a more flat landing pad — a method I developed without even understanding what I was doing.
If you know any Persians (Iranians) ask them to do the Beshkan for you. It is a two handed snapping technique that is 5x louder than our western version. Here’s a Persian site that explains it, even includes a video (link on the right): http://ajabanzaban.com/culture/beshkan.html
photo from whatbettertime @ Flickr