Vol. 13, No. 2, 2020

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Spherical half-designs of high order

Daniel Hughes and Shayne Waldron

Vol. 13 (2020), No. 2, 193–203
Abstract

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 3 based on the pentakis dodecahedron. This gives rise to a 32-point weighted spherical 9-design for the sphere.

Keywords
spherical $t$-designs, spherical half-designs, tight spherical designs, finite tight frames, integration rules, cubature rules, cubature rules for the sphere, pentakis dodecahedron
Mathematical Subject Classification 2010
Primary: 05B30, 42C15, 65D30
Secondary: 94A12
Milestones
Received: 5 September 2018
Revised: 3 June 2019
Accepted: 4 November 2019
Published: 30 March 2020

Communicated by David Royal Larson
Authors
Daniel Hughes
Department of Mathematics
University of Auckland
Auckland
New Zealand
Shayne Waldron
Department of Mathematics
University of Auckland
Auckland
New Zealand