  We compute all isomorphism classes of simplicial arrangements in the real
projective plane with up to 27 lines. It turns out that Gr\"unbaums catalogue
is complete up to 27 lines except for four new arrangements with 22, 23, 24, 25
lines, respectively. As a byproduct we classify simplicial arrangements of
pseudolines with up to 27 lines. In particular, we disprove Gr\"unbaums
conjecture about unstretchable arrangements with at most 16 lines, and prove
the conjecture that any simplicial arrangement with at most 14 pseudolines is
stretchable.
