The linear Turán number of small triple systems or why is the wicket interesting?

A linear triple system is a 3-uniform hypergraph H=(V,E), where E is a set of three-element subsets of V such that any two edges intersect in at most one vertex. For linear triple systems H,F we say that H is F-free if H does not contain any subsystem isomorphic to F. We consider F fixed and call it a configuration. The (linear) Turán number exL(n,F) (or simply just ex(n,F)) of a configuration F is the maximum number of edges in F-free linear triple systems with n vertices.