# Optimal number of points for integration over the surface of a sphere

My objetive is to calculate overlapping between spheres. What is the minimum number of points to allocate in the surface of a sphere, so we can perform numerical integration over each sphere with the highest possible accuracy? Should they be distributed randomly of following some criteria? Which are the best algorithms for this?

PS: A clear example of what I am looking for is related to this. Lebedev uses some idea to generate up to 30 something points which warranties some good accuracy

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The accuracy increases with the number of points; there's no highest possible accuracy and thus no minimum number of points for highest possible accuracy. –  joriki Jul 12 '11 at 9:34
A search for 'numerical integration on the sphere' turns up lots of links, most of which relate to your last two questions, for instance maths.sussex.ac.uk/preprints/document/SMRR-2009-22.pdf –  joriki Jul 12 '11 at 9:39
Plus the volume can be solved analytically. –  anon Jul 12 '11 at 9:42
For both volume and surface the case is overlapping between spheres, so it is not so straightforward –  flow Jul 12 '11 at 9:47
Spherical designs are a fun construction. They are guaranteed to give exact results for polynomial functions up to a certain degree, but may not be quite what you want? –  Jyrki Lahtonen Jul 12 '11 at 10:00