Abstract:
A new lower bound is obtained for the cardinality of spherical designs. In its dependence on dimension it improves the well-known bound of Delsarte by an exponential factor as the degree of the design tends to infinity.
This publication is cited in the following 26 articles:
Peter Boyvalenkov, Danila Cherkashin, “The Kissing Number in 48 Dimensions for Codes with Certain Forbidden Distances is 52 416 000”, Results Math, 80:1 (2025)
Dmitriy Bilyk, Alexey Glazyrin, Ryan W. Matzke, Josiah Park, Oleksandr Vlasiuk, 2023 57th Asilomar Conference on Signals, Systems, and Computers, 2023, 522
Boyvalenkov P., Delchev K., Jourdain M., “Upper Energy Bounds For Spherical Designs of Relatively Small Cardinalities”, Discret. Comput. Geom., 65:1 (2021), 244–260
Steinerberger S., “Spectral Limitations of Quadrature Rules and Generalized Spherical Designs”, Int. Math. Res. Notices, 2021:16 (2021), 12265–12280
Boyvalenkov P., Stoyanova M., “Linear Programming Bounds For Covering Radius of Spherical Designs”, Results Math., 76:2 (2021), 95
I. A. Martyanov, “Reshenie zadachi Delsarta dlya $4$-dizainov na sfere $\mathbb{S}^{2}$”, Chebyshevskii sb., 22:3 (2021), 154–165
Steinerberger S., “Generalized Designs on Graphs: Sampling, Spectra, Symmetries”, J. Graph Theory, 93:2 (2020), 253–267
Jianfeng Lu, Matthias Sachs, Stefan Steinerberger, “Quadrature Points via Heat Kernel Repulsion”, Constr Approx, 51:1 (2020), 27
Robert S. Womersley, Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, 1243
Brauchart J.S., Grabner P.J., “Distributing Many Points on Spheres: Minimal Energy and Designs”, J. Complex., 31:3 (2015), 293–326
Andriy Bondarenko, Danylo Radchenko, Maryna Viazovska, “Optimal asymptotic bounds for spherical designs”, Ann. Math, 178:2 (2013), 443
A. V. Bondarenko, D. V. Gorbachev, “Minimal Weighted $4$-Designs on the Sphere $S^2$”, Math. Notes, 91:5 (2012), 738–741
Boyvalenkov P., Stoyanova M., “A new asymptotic bound of the minimum possible odd cardinality of spherical (2k-1)-designs”, Discrete Mathematics, 310:15–16 (2010), 2170–2175
Bannai, E, “A survey on spherical designs and algebraic combinatorics on spheres”, European Journal of Combinatorics, 30:6 (2009), 1392
Lyubich, YI, “Lower bounds for projective designs, cubature formulas and related isometric embeddings”, European Journal of Combinatorics, 30:4 (2009), 841
A J Scott, “Optimizing quantum process tomography with unitary 2-designs”, J Phys A Math Theor, 41:5 (2008), 055308
St. Petersburg Math. J., 18:1 (2007), 119–139
V. A. Yudin, “Distribution of the points of a design on the sphere”, Izv. Math., 69:5 (2005), 1061–1079
Samorodnitsky A., “On linear programming bounds for spherical codes and designs”, Discrete & Computational Geometry, 31:3 (2004), 385–394
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