Tight spherical designs, I
نویسندگان
چکیده
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 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...
متن کاملNew spherical 4-designs
Hardin, R.H. and N.J.A. Sloane, New spherical 4-designs, Discrete Mathematics 106/107 (1992) 255-264. This paper gives a number of new spherical 4-designs, and presents numerical evidence that spherical 4-designs containing n points in k-dimensional space with k G 8 exist precisely for the following values of n and k: n even and 22 for k = 1; n 2 5 for k = 2; n = 12, 14, >I6 for k=3;n~2Ofork=4;...
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.
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1979
ISSN: 0025-5645
DOI: 10.2969/jmsj/03110199