Lemmens and Seidel's conjecture for equiangular lines with common angle $1/5$

Let $M_a(n)$ denote the maximum number of equiangular lines in $\boldsymbol{R}^n$ with common angle $a$. Lemmens and Seidel's conjecture.

$$M_{1/5}(n)=\begin{cases}276&\text{for }23\leq n\leq185;\left\lfloor\frac{3}{2}(n-1)\right\rfloor&\text{for }n\geq185. \end{cases}$$

Lemmens and Seidel obtained results leading to this conjecture through their pillar-decomposition method for relative bounds on equiangular lines. The conjectured values concern dimensions $n\geq23$ and remain unresolved in general.