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An extension is given of a recent result of Glazyrin, showing that an orthonormal basis $\{e_{i}\}_{i=1}^{d}$ joined with the vectors $\{e_{j}\}_{j=1}^{m}$, where $1\leq m < d$ minimizes the $p$-frame potential for $p\in[1,2\log{\frac{2m+1}{2m}}/\log{\frac{m+1}{m}}]$ over all collections of $N=d+m$ vectors $\{x_1,\dots,x_N \}$ in $\mathbb{S}^{d-1}$.
Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem)
D. Hilbert · 1909
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Equiangular lines
P. W. H. Lemmens, J. J. Seidel · 1973
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Cubature Formulae, Polytopes, and Spherical Designs. The Geometric Vein. (1981), 203–218
J. M. Goethals & J. J. Seidel · 1981
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Isometric Embeddings and Cubature Formulas over Classical Fields
O. Shatalova · 2001
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M. Ehler & K. A. Okoudjou · 2012
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Optimal simplices and codes in projective spaces Geom. Topol. 20
H. Cohn, A. Kumar, & G. Minton · 2016
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Universal Optimal Configurations for the p-Frame Potentials
X. Chen, V. Gonzales, E. Goodman, S. Kang, & K. Okoudjou · 2019
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Minimizing the p p -frame potential
A. Glazyrin · 2019
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