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arXiv · 2607.23897

Biangular lines with angles arccos(1/5) and arccos(3/5)

Paul Tricot
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Abstract

The largest known biangular lines systems in dimension 7 through 20 are due to Ganzhinov and Sz\"oll\H{o}si, and the lines make angles $\arccos(\frac{1}{5})$ and $\arccos(\frac{3}{5})$. They are constructed by making use of the nice connection with integral lattices. We explore further the connection between biangular lines and integral lattices to classify the largest biangular line systems with these angles, in dimension 7 through 10. We also give a new biangular line system in dimension 15, that matches the size of the largest known in this dimension.

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Paul Tricot. 2026-07-27. Biangular lines with angles arccos(1/5) and arccos(3/5). https://arxiv.org/abs/2607.23897

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