Terao's freeness conjecture for arrangements of 15 and 16 lines

We prove that Terao's freeness conjecture holds for arrangements of 15 and of 16 lines in the complex projective plane. Together with the theorem of Barakat and Kühne for at most 14 hyperplanes, this shows that freeness of a central arrangement of at most 16 planes in $\mathbb{C}^3$ is determined by