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A symmetric conference matrix of order 86
Abstract
We construct a symmetric conference matrix of order $86$, the smallest order for which existence was open. Equivalently, there exist a conference graph with parameters $(85,42,20,21)$, a regular two-graph on $86$ points, and a real equiangular tight frame of $86$ vectors in ℝ43. The matrix is a 12×12 array of 7×7 circulants with two border rows, and it admits a group of automorphisms of order $21$. Its $86$ descendants give exactly ten nonisomorphic strongly regular graphs.
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BibTeX
@misc{verma2026symmetric,
title = {{A symmetric conference matrix of order 86}},
author = {Harshit Verma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08893},
eprint = {2610.08893},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08893},
}
RIS
TY - UNPB
TI - A symmetric conference matrix of order 86
AU - Harshit Verma
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08893
UR - https://arxiv.org/abs/2610.08893
AB - We construct a symmetric conference matrix of order $86$, the smallest order for which existence was open. Equivalently, there exist a conference graph with parameters $(85,42,20,21)$, a regular two-graph on $86$ points, and a real equiangular tight frame of $86$ vectors in ℝ^43. The matrix is a 12×12 array of 7×7 circulants with two border rows, and it admits a group of automorphisms of order $21$. Its $86$ descendants give exactly ten nonisomorphic strongly regular graphs.
ER -