On Tight Euclidean 6-Designs: An Experimental Result
DOI:
https://doi.org/10.5614/itbj.sci.2011.43.1.3Abstract
A finite set n X ? n with a weight function w: X ? > 0 is called Euclidean t-design in > 0 (supported by p concentric spheres) if the following condition holds: 1 i p i i i S x X w X f d w f S ? x x x x for any polynomial f(x) ?Pol > 0 of degree at most t. Here Si n is a sphere of radius ri 0, Xi=X S, and i(x) is an O(n) -invariant measure on Si such that |Si|=rin-1|Sn-1>|, with |Si| is the surface area of Si and |Sn-1|is a surface area of the unit sphere in n. Recently, Bajnok [1] constructed tight Euclidean t-designs in the plane (n=2) for arbitrary t and p . In this paper we show that for case t=6 and p=2 , tight Euclidean 6-designs constructed by Bajnok is the unique configuration in ?n, for 2 n 8.References
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