Spherical Design

$X$ 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,

$${1\over{\rm volume}\ E}\int_E f(\xi)\,d\xi={1\over\vert X\vert}\sum_{x\in X} f(x).$$

References

Colbourn, C. J. and Dinitz, J. H. (Eds.) ``Spherical $t$-Designs.'' Ch. 44 in CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, pp. 462-466, 1996.