X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In other words, 1/(Vol(E)) integral_E f(ξ) d ξ = 1/( left bracketing bar X right bracketing bar ) sum_(x element X) f(x). Spherical t-designs give the placement of n points on a sphere for use in numerical integration with equal weights.
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