  We introduce a greedy algorithm optimizing arrangements of lines with respect
to a property. We apply this algorithm to the case of simpliciality: it
recovers all known simplicial arrangements of lines in a very short time and
also produces a yet unknown simplicial arrangement with 35 lines. We compute a
(certainly incomplete) database of combinatorially simplicial complex
arrangements of hyperplanes with up to 50 lines. Surprisingly, it contains
several examples whose matroids have an infinite space of realizations up to
projectivities.

Combinatorics