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Spherical
half-designs of high order
Daniel Hughes and Shayne Waldron
Vol. 13 (2020), No. 2, 193–203
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Abstract |
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We give some explicit examples of putatively optimal spherical half-designs, i.e., ones for which there is numerical evidence that they are of minimal size. These include a 16-point weighted spherical half-design of order 8 for based on the pentakis dodecahedron. This gives rise to a 32-point weighted spherical 9-design for the sphere. |
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Keywords
spherical $t$-designs, spherical half-designs, tight
spherical designs, finite tight frames, integration rules,
cubature rules, cubature rules for the sphere, pentakis
dodecahedron
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Mathematical Subject Classification 2010
Primary: 05B30, 42C15, 65D30
Secondary: 94A12
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Milestones
Received: 5 September 2018
Revised: 3 June 2019
Accepted: 4 November 2019
Published: 30 March 2020
Communicated by David Royal Larson
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Authors |
| Daniel Hughes | |
| Department of Mathematics University of Auckland Auckland New Zealand |
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| Shayne Waldron | |
| Department of Mathematics University of Auckland Auckland New Zealand |
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