2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146017There 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.11 pages, 8 figures, added pseudoline realizations by Branko Gr{ü}nbaumMetric Geometry52C30 (Primary), 05B30 (Secondary)text