发表机构
NXP Semiconductors; Harvard Business School; Center of Mathematical Sciences and Applications, Harvard University; Technological Innovation, Entrepreneurship, and Strategic Management (TIES) Group at the MIT Sloan School of Management（恩智浦半导体; 哈佛商学院; 哈佛大学数学科学与工程应用中心; 麻省理工学院斯隆管理学院技术创新、创业与战略管理（TIES）小组）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种素数维度整数格族，其亲吻常数下界达到 $e^{\sqrt{n}}$ 量级，优于 Barnes-Wall 格，基于 Reed-Solomon 码推广构造。
AI 中文摘要
对于素数维度 $n \ge 5$，我们定义了整数格 $\mathcal{L}_n$，其亲吻常数满足 \begin{align} \tau(\mathcal{L}_n) \ge \left(\frac{1}{\sqrt{2 \pi e}} + o(1)\right) n^{3/4} e^{\sqrt n}。 \notag \end{align} 这改进了 Barnes-Wall 格的增长率 $e^{\Theta((\log n)^2)}$，后者此前提供了已知最佳的渐近下界。该构造是 Bennett-Peikert 基于 Reed-Solomon 码的先前构造的推广。
英文摘要
For all prime powers $q\geq5$, we construct lattices $\mathcal{L}_q\subseteq\mathbb{Z}^q$ with kissing numbers \[ τ(\mathcal{L}_q)\geq \left(\frac{1}{2πe^2}+o(1)\right)\sqrt{q}\,e^{2\sqrt{q}}. \] The same asymptotic bound holds on a set of integer dimensions of natural density $1$, and in every sufficiently large integer dimension $n$ with an additional factor $e^{-\tfrac{1}{2}n^{1/40}}$. The construction is an extension of a previous construction by Bennett-Peikert based on Reed-Solomon codes.
Commentsv1 contained a construction with $τ(\mathcal{L}_n) \ge e^{\sqrt{n}}$; v2 improves the constant in the exponent by a factor $2$
