The upper-bound conjecture for equiangular lines in dimensions 8 through 13

Let $t'_n$ denote the largest number of lines in an equiangular family obtained from the minimal vectors of a lattice in dimension $n$. Dimension $8$–$13$ conjecture. For $8\le n\le 13$ we have

$$t'_n\le 2n,$$

and $t'_{13}=26$. This is motivated by lower bounds $t'_n\ge 2(n-1)$ and computational experiments with classical lattices of minimum $4$; the source gives no resolution of the conjecture.