  A long standing question is if maximum number $\mu(d)$ of nodes on a surface
of degree $d$ in $\dP^3(\dC)$ can be achieved by a surface defined over the
reals which has only real singularities. The currently best known asymptotic
lower bound, $\mu(d) \gtrapprox {5/12}d^3$, is provided by Chmutov's
construction from 1992 which gives surfaces whose nodes have non-real
coordinates. Using explicit constructions of certain real line arrangements we
show that Chmutov's construction can be adapted to give only real
singularities. All currently best known constructions which exceed Chmutov's
lower bound (i.e., for $d=3,4,...,8,10,12$) can also be realized with only real
singularities. Thus, our result shows that, up to now, all known lower bounds
can be attained with only real singularities. We conclude with an application
of the theory of real line arrangements which shows that our arrangements are
aymptotically the best possible ones. This proves a special case of a
conjecture of Chmutov.
