Delsarte problem for 4-designs on the unit 3-sphere
https://doi.org/10.22405/2226-8383-2022-23-4-157-161
Abstract
The extremal Delsarte problem 𝐴(𝑑, 𝑠) for spherical 𝑠-designs allows us to estimate from below the minimum number of nodes 𝑁(𝑑, 𝑠) of a weighted quadrature formula on the sphere S𝑑.
We prove that 𝐴(3, 4) = 14.560317967882 . . . .
Hence 𝑁(3, 4) > 15. Our open conjecture is that 𝑁(3, 4) = 16.
Supporting agencies: This Research was performed by a grant of Russian Science Foundation (project 18-11-00199), https://rscf. ru/project/18-11-00199/.
About the Authors
Dmitriy Victorovich Gorbachev
Tula State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Ivan Anatol’evich Martyanov
Tula State University
Russian Federation
Russian Federation
postgraduate student
References
1. Martyanov, I.A. 2021. “Solving the Delsarte problem for 4-designs on the sphere 𝑆2”, Chebyshevskii
2. Sbornik, vol. 22, no. 3, pp. 154–165. (In Russ.)
Review
For citations:
Gorbachev D.V., Martyanov I.A. Delsarte problem for 4-designs on the unit 3-sphere. Chebyshevskii Sbornik. 2022;23(4):157-161. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-157-161
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