{"paper":{"title":"There are no 76 equiangular lines in $R^{19}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Wei-Hsuan Yu","submitted_at":"2015-11-27T06:50:37Z","abstract_excerpt":"Maximum size of equiangular lines in $\\mathbb{R}^{19}$ has been known in the range between 72 to 76 since 1973. Acoording to the nonexistence of strongly regular graph $(75,32,10,16)$ \\cite{aza15}, Larmen-Rogers-Seidel Theorem \\cite{lar77} and Lemmen-Seidel bounds on equiangular lines with common angle $\\frac 1 3$ \\cite{lem73}, we can prove that there are no 76 equiangular lines in $\\mathbb{R}^{19}$. As a corollary, there is no strongly regular graph $(76,35,18,14)$. Similar discussion can prove that there are no 96 equiangular lines in $\\mathbb{R}^{20}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08569","kind":"arxiv","version":2},"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"}