  We find a surface of degree 7 in real projective three-space P^3(R) with 99
real nodes within a family of surfaces with dihedral symmetry: First, we
consider this family over some small prime fields, which allows us to test all
possible parameter sets using computer algebra. In this way we find some
examples of 99-nodal surfaces over some of these finite fields. Then, the
examination of the geometry of these surfaces allows us to determine the
parameters of a 99-nodal septic in characteristic zero. This narrows the
possibilities for \mu(7), the maximum number of nodes on a septic, to: 99 <=
\mu(7) <= 104. When reducing our surface modulo 5, we even obtain a 100-nodal
septic in P^3(F_5).
