Some blocking semiovals of homology type in planes of square order

Abstract

A blocking semioval in a projective plane is a set of points which is both a semioval and a blocking set. In this paper, blocking semiovals in the Desaguesian projective plane PG(2, s^2) admitting an order s+1 homology group are considered. The geometry of the point-orbits of such a group is studied. Using this geometry two new blocking semiovals are constructed in PG(2, 5^2). Their automorphism group is also discussed

Blocking structures in finite projective planes

“…See also [5], [11], for the Desarguesian case. Many constructions of blocking semiovals are known, see [9], [16] and references therein. the vertexless triangle with size 3 − 3, > 2.…”

“…the vertexless triangle with size 3 − 3, > 2. Many constructions of blocking semiovals are known, see [9], [16] and references therein. However, apart from sporadic examples [15,17], not many examples of blocking semiovals are known to exist in non-Desarguesian planes.…”