{"paper":{"title":"Efficient Spherical Designs with Good Geometric Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Robert S. Womersley","submitted_at":"2017-09-05T23:28:22Z","abstract_excerpt":"Spherical $t$-designs on $\\mathbb{S}^{d}\\subset\\mathbb{R}^{d+1}$ provide $N$ nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of degree at most $t$. This paper considers the generation of efficient, where $N$ is comparable to $(1+t)^d/d$, spherical $t$-designs with good geometric properties as measured by their mesh ratio, the ratio of the covering radius to the packing radius. Results for $\\mathbb{S}^{2}$ include computed spherical $t$-designs for $t = 1,...,180$ and symmetric (antipodal) $t$-designs for degrees up to $325$, all with low mesh r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01624","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}