Determine whether 57 equiangular lines are maximal in dimension 18

Determine whether N(18)=57; equivalently, prove or disprove that no set of more than 57 equiangular lines exists in real dimension 18.

Background

The paper establishes 57 ≤ N(18) ≤ 59 and constructs numerous strongly maximal sets of 57 equiangular lines. Strong maximality of these particular sets does not rule out the existence of an unrelated set with 58 or 59 lines. The authors therefore indicate that the equality N(18)=57 may hold, but leave it unresolved.