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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).


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.

© 1996-9 Eric W. Weisstein