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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 ex L (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. Here we call attention to some properties of the wicket W , formed by three rows and two columns of a 3 × 3 point matrix. On one hand we show that the problem whether ex (n , F) = o (n 2) can be decided for all configurations with at most five edges, except for F = W , which remains undecided. On the other hand we prove that ex (n , W) ≤ (1 − c) n 2 6 with some c > 0 , separating it from the conjectured asymptotic of ex (n , G 3 × 3) , where G 3 × 3 , the grid , formed by three rows and three columns of a 3 × 3 point matrix. [ABSTRACT FROM AUTHOR]