  We show a one-to-one correspondence between arrangements of d lines in the
projective plane, and lines in P^{d-2}. We apply this correspondence to
classify (3,q)-nets over the complex numbers for all q<=6. When q=6, we have
twelve possible combinatorial cases, but we prove that only nine of them are
realizable. This new case shows several new properties for 3-nets: different
dimensions for moduli, strict realization over certain fields, etc. We also
construct a three dimensional family of (3,8)-nets corresponding to the
Quaternion group.
