Abstract
This paper examines subsets with at most n points on a line in the projective plane . A lower bound for the size of complete ‐arcs is established and shown to be a generalisation of a classical result by Barlotti. A sufficient condition ensuring that the trisecants to a complete (k, 3)‐arc form a blocking set in the dual plane is provided. Finally, combinatorial arguments are used to show that, for , plane (k, 3)‐arcs satisfying a prescribed incidence condition do not attain the best known upper bound.
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