Complex multiangular line systems and sphere packings

• Project/Area Number: 24K06829
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12030:Basic mathematics-related
• Research Institution: Shimane University
• Principal Investigator: SZOLLOSI FERENC 島根大学, 学術研究院理工学系, 講師 (50895985)
• Project Period (FY): 2024-04-01 – 2029-03-31
• Project Status: Granted (Fiscal Year 2024)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2028: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2027: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2026: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2025: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2024: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: Multiangular lines / Sphere packings / Computation

Outline of Research at the Start

This project aims to study dense packings of congruent objects in the Euclidean space. The most important objects of interest are hyperspheres, whose packings give rise to error-correcting communication protocols which are widely employed today. Since different packings might lead to protocols differing in efficiency, reliability, and fitness for a given purpose, our aim is to find, in some sense, the best possible packings. The main tools we use is a family of highly symmetrical complex unit vectors.