A minimum blocking semioval in PG(2, 9)
- 61 Downloads
A blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (i.e., there is a unique tangent line at each point). The minimum size of a blocking semioval is currently known in all projective planes of order < 11, with the exception of PG(2, 9). In this note we show by demonstration of an example that the smallest blocking semioval in PG(2, 9) has size 21 and investigate some properties of this set.
Mathematics Subject Classification51E20
Unable to display preview. Download preview PDF.
- 1.Baker, R.D., Ebert, G.L., Korchmáros, G., Szőnyi, T.: Orthogonally divergent spreads of Hermitian curves. In: De Clerck, F., et al. (ed.) Finite Geometry and Combinatorics, pp. 17–30. Cambridge University Press, Cambridge (1993)Google Scholar
- 2.Bartoli, D.: On the structure of semiovals of small size. J. Comb. Des. (to appear). doi: 10.1002/jcd.21383
- 9.Kiss, G., Marcugini, S., Pambianco, F.: On the spectrum of the sizes of semiovals in PG(2, q), q odd. Discret. Math. 310(22), 3188–3193 (2010)Google Scholar