Grünbaum's catalogue conjecture for simplicial line arrangements

A simplicial line arrangement is a finite arrangement of lines in $\mathbb{P}^{2}_{\mathbb{R}}$ whose complement has only open triangular connected components. Grünbaum's catalogue consists of three infinite families together with approximately $90$ sporadic examples. Grünbaum's catalogue conjecture. Except for finitely many corrections, Grünbaum's catalogue is complete. Equivalently, one expects that there are only three infinite families of simplicial line arrangements. The paper studies this classification problem and provides a complete classification of nearly free, non-free simplicial arrangements with at most $27$ lines; the source gives no resolution of the catalogue conjecture itself.