Füredi–Lagarias–Morgan exponential bound for equilateral sets in strictly convex spaces

Let $X$ be a strictly convex $n$-dimensional Minkowski space. Füredi–Lagarias–Morgan conjecture. There exists some constant $\varepsilon>0$ such that

$$e(X)\leq (2-\varepsilon)^n.$$

The conjecture would improve the general upper bound for equilateral sets in strictly convex normed spaces. The source does not indicate whether it has been resolved.