The Lemmens–Seidel conjecture for equiangular lines at angle arccos(1/5)

Let $N_{\alpha}(r)$ be the maximum number of a system of equiangular lines in $\mathbb{R}^r$ with common angle $\arccos\alpha$. The Lemmens–Seidel conjecture concerns the case $\alpha=\frac{1}{5}$. Lemmens–Seidel conjecture. The maximum cardinality of a system of equiangular lines with angle $\arccos\frac{1}{5}$ in $\mathbb{R}^r$ is $276$ for $23 \leqslant r \leqslant 185$, and $\lfloor \frac{3r-3}{2}\rfloor$ for $r \geqslant 185$. Neumaier proved the assertion for sufficiently large $r$, and the paper states that it completely solves the conjecture.