A Lower Bound on Blocking Semiovals

A semioval in a projective plane Π is a set S of points such that for every pointP ∈ S, there exists a unique line ℓ of Π such thatℓ ∩ S = { P }. In other words, at every point of S, there exists a unique tangent line. A blocking set in Π is a set B of points such that every line ofΠ contains at least one point of B, but is not entirely contained in B. Combining these notions, we obtain the concept of a blocking semioval, a set of points in a projective plane which is both a semioval and a blocking set. Batten indicated applications of such sets to cryptography, which motivates their study. In this paper, we give some lower bounds on the size of a blocking semioval, and discuss the sharpness of these bounds.