{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/better-lattice-quantizers-constructed-from","title":"Better Lattice Quantizers Constructed from Complex Integers","arxiv_id":"2204.01105","date":"2022-04-03","proceeding":null,"authors":["Shanxiang Lyu","Zheng Wang","Cong Ling","Hao Chen"],"abstract":"This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices $\\mathcal{E}_{m}$ and $\\mathcal{G}_{m}$. By explicitly linking their lattice bases to various forms of $\\mathcal{E}_{m}$ and $\\mathcal{G}_{m}$ cosets, we discover the $\\mathcal{E}_{m,2}^+$ lattices, based on which we report the best known lattice quantizers in dimensions $14$, $15$, $18$, $19$, $22$ and $23$. Fast quantization algorithms of the generalized checkerboard lattices are proposed to enable evaluating the normalized second moment (NSM) through Monte Carlo integration.","url_abs":"https://arxiv.org/abs/2204.01105v3","url_pdf":"https://arxiv.org/pdf/2204.01105v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"better-lattice-quantizers-constructed-from","repo_url":"https://github.com/shx-lyu/latticequantizer","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}