There are no realizable 154- and 164-configurations
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 > k2+k-5 holds.
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