  There exist a finite number of natural numbers n for which we do not know
whether a realizable n_4-configuration does exist. We settle the two smallest
unknown cases n=15 and n=16. In these cases realizable n_4-configurations
cannot exist even in the more general setting of pseudoline-arrangements. The
proof in the case n=15 can be generalized to n_k-configurations. We show that a
necessary condition for the existence of a realizable n_k-configuration is that
n > k^2+k-5 holds.
