Year: 2026
Type: preprint
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 $\mathbb{R}^{43}$. The matrix is a $12\times12$ array of $7\times7$ 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.
Source: arXiv (Cornell University)
Author: Verma, Harshit
Institution: Yale University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221037321