Equiangular lines in Euclidean spaces: dimensions 17 and 18
Gary R.W. Greaves, Jeven Syatriadi, Pavlo Yatsyna
TL;DR
This paper determines the maximum number of equiangular lines in 17 dimensions as 48 and provides an explicit construction for 18 dimensions with at least 57 lines, solving longstanding open problems.
Contribution
It establishes the exact maximum for 17 dimensions and improves the lower bound for 18 dimensions with explicit constructions.
Findings
Maximum equiangular lines in 17D is 48.
Explicit construction of at least 57 lines in 18D.
Solved a longstanding open problem in the field.
Abstract
We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem. Furthermore, by giving an explicit construction, we improve the lower bound on the maximum cardinality of an equiangular line system in 18 dimensions to 57.
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Taxonomy
TopicsFinite Group Theory Research · Point processes and geometric inequalities · Mathematical Approximation and Integration