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- Spherical_design abstract "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). Such a set is often called a spherical t-design to indicate the value of t, which is a fundamental parameter. Spherical t-designs for different values of N and t can be found precomputed at http://www.research.att.com/~njas/sphdesigns.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.The concept of a spherical design is due to Delsarte, Goethals, and Seidel (1977). The existence and structure of spherical designs with d = 1 (that is, in a circle) was studied in depth by Hong (1982).".
- Spherical_design wikiPageExternalLink sphdesigns..
- Spherical_design wikiPageID "9730285".
- Spherical_design wikiPageRevisionID "606717722".
- Spherical_design hasPhotoCollection Spherical_design.
- Spherical_design subject Category:Algebra.
- Spherical_design subject Category:Design_of_experiments.
- Spherical_design comment "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). Such a set is often called a spherical t-design to indicate the value of t, which is a fundamental parameter.".
- Spherical_design label "Spherical design".
- Spherical_design sameAs m.02pqg16.
- Spherical_design sameAs Q7576703.
- Spherical_design sameAs Q7576703.
- Spherical_design wasDerivedFrom Spherical_design?oldid=606717722.
- Spherical_design isPrimaryTopicOf Spherical_design.