Spherical Design
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High Quality Content by WIKIPEDIA articles! A spherical design, part of combinatorial design theory in mathematics, is a finite set of N points on the d-dimensional unit hypersphere Sd such that the average value of any polynomial f of degree t or less on the set equals the average value of f on the whole sphere (that is, the integral of f over Sd divided by the area or measure of Sd).Spherical designs can be of value in approximation theory, in statistics for experimental design (being usable to construct rotatable designs), in combinatorics, and in geometry. The main problem is to find examp...
High Quality Content by WIKIPEDIA articles! A spherical design, part of combinatorial design theory in mathematics, is a finite set of N points on the d-dimensional unit hypersphere Sd such that the average value of any polynomial f of degree t or less on the set equals the average value of f on the whole sphere (that is, the integral of f over Sd divided by the area or measure of Sd).Spherical designs can be of value in approximation theory, in statistics for experimental design (being usable to construct rotatable designs), in combinatorics, and in geometry. The main problem is to find examples, given d and t, that are not too large. However, such examples may be hard to come by. Spherical t-designs have also recently been appropriated in quantum mechanics in the form of quantum t-designs with various applications to quantum information theory, quantum computing and POVMs.
