Abstract
According to Delsarte, Goethals, and Seidel, a nonempty subset X of the set of unit vectors in the real vector space R d of dimension d is called a tight spherical t-design if (i) Σ α∈ X W( α) = 0 for all homogeneous harmonic polynomials W( α) in R d of degree 1,2,…, t, and (ii) |X|=( d+e−1 d−1 )+( d+e−2 d−1 ), |X|=2( d+e−1 d−1 ) for t = 2 e and t = 2 e + 1, respectively. In this paper, we show that if t = 2 e, e ⩾ 3 or t = 2 e + 1, e ⩾ 4, and if there exists a tight spherical t-design, then the dimension d is bounded by a certain function depending only on t.
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