There are no 76 equiangular lines in R¹⁹

2015/11/27 by Yu, Wei-Hsuan
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1511.08569

Abstract

Maximum size of equiangular lines in ℝ¹⁹ has been known in the range between 72 to 76 since 1973. Acoording to the nonexistence of strongly regular graph (75,32,10,16) \citeaza15, Larmen-Rogers-Seidel Theorem \citelar77 and Lemmen-Seidel bounds on equiangular lines with common angle \frac 1 3 \citelem73, we can prove that there are no 76 equiangular lines in ℝ¹⁹. As a corollary, there is no strongly regular graph (76,35,18,14). Similar discussion can prove that there are no 96 equiangular lines in ℝ²⁰.

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