{"paper":{"title":"Dense lattices in low dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hao Chen","submitted_at":"2013-06-11T16:06:17Z","abstract_excerpt":"The Barnes-Wall lattice ${\\bf \\Lambda}_{16}$ with the center density ${\\{1}{16}}$ and the kissing number 4320 was found in 1959 and is the only known densest sphere packing in the dimension 16. J. H. Conway and N.J.A. Sloane conjectured that ${\\bf \\Lambda}_{16}$ is the densest 16 dimensional lattice. Sometimes it is conjectured that the Barnes-Wall lattice ${\\bf \\Lambda}_{16}$ is the only densest lattice and the optimal sphere packing in ${\\bf R}^{16}$. In this paper two new 16 dimensional lattices with the center density $\\{1}{16}$ and the kissing numbers 4224 and 4176 are constructed. This l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2568","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"}