منابع مشابه
On Tight Spherical Designs
Let X be a tight t-design of dimension n for one of the open cases t = 5 or t = 7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to exclude infinitely many values for n.
متن کاملThe Nonexistence of Certain Tight Spherical Designs
In this paper, the nonexistence of tight spherical designs is shown in some cases left open to date. Tight spherical 5-designs may exist in dimension n = (2m + 1)2 − 2, and the existence is known only for m = 1, 2. In the paper, the existence is ruled out under a certain arithmetic condition on the integer m, satisfied by infinitely many values of m, including m = 4. Also, nonexistence is shown...
متن کامل7 on Tight Projective Designs
It is shown that among all tight designs in FP n = RP 1 , where F is R or C, or H (quaternions), only 5-designs in CP 1 [14] have irrational angle set. This is the only case of equal ranks of the first and the last irreducible idempotent in the corresponding Bose-Mesner algebra.
متن کاملExtremal Spherical Designs on S
A spherical t-design is a system of m points on the unit sphere S ⊂ R such that the equal weight cubature rule (|S2|/m) mj=1 f(xj) gives ∫ S2 f(x)dx for all polynomials f of degree at most t. Typically the interest is in finding spherical t-designs with the smallest number of points. Goethals and Seidel proved a lower bound m ≥ t/4 + O(t), which is not achievable for t ≥ 3. Upper bounds of m = ...
متن کاملTight Gaussian 4-Designs
A Gaussian t-design is defined as a finite set X in the Euclidean space Rn satisfying the condition: 1 V (Rn ) ∫ Rn f (x)e −α2||x ||2 dx = u∈X ω(u) f (u) for any polynomial f (x) in n variables of degree at most t , here α is a constant real number and ω is a positive weight function on X . It is easy to see that if X is a Gaussian 2e-design in Rn , then |X | ≥ (n+e e ) . We call X a tight Gaus...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1979
ISSN: 0097-3165
DOI: 10.1016/0097-3165(79)90052-9