I wrote a short collection of notes that describe how to use the Hammersley point set in 2d for generating fast sampling points on the hemisphere. The notes can be found at
The Hammersley point set is one of the simplest quasi-Monte Carlo sampling patterns and in 2d it can be efficiently generated with a couple of bit operations (and some floating point multiplications). It is thus a good candidate when some 2d sampling pattern is needed inside a shader program and is a good alternative to using a look-up table in many applications. The article focuses mainly on generating sampling points on the hemisphere but the point set can of course be used for many other applications like shadow map filtering or screen space ambient occlusion.
Here is an image of the pattern for 16 points: