ABSTRACT. There exist a finite number of natural numbers n for which we do not know whether a realizable n4-configuration does exist. We settle the two smallest unknown cases n = 15 and n = 16. In these cases realizable n4-configurations cannot exist even in the more general setting of pseudoline-arrangements. The proof in the case n = 15 can be generalized to nk-configurations. We show that a necessary condition for the existence of a realizable nk-configuration is that n> k 2 + k − 5 holds. 1
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