Determine the maximum number of equiangular lines in dimension 18

Determine the exact value of N(18), the maximum cardinality of a set of equiangular lines in real dimension 18.

Background

The paper identifies dimension 18 as the smallest dimension in which the maximum number N(d) of equiangular lines remains unresolved. At the time of the paper, the authors establish the bounds 57 ≤ N(18) ≤ 59, with the lower bound supplied by previously constructed sets of 57 equiangular lines and the upper bound obtained through refinements of the relative bound. The constructions in the paper produce many additional sets of 57 lines, but all are strongly maximal, so they do not determine whether sets of 58 or 59 lines exist.