Jeremy M. Dover

A Lower Bound on Blocking Semiovals

A semioval in a projective plane ? is a set S of points such that for every pointP?S, there exists a unique line ? of ? such that??S= { P }. In other words, at every point of S, there exists a unique tangent line. A blocking set in ? is a set B of points such that every line of? 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.

Some Sets of Type (m,n) in Cubic Order Planes

AbstractA (4,9)-set of size 829 in

Hyperbolic Fibrations ofPG(3,q)

\mathcal{P}\mathcal{G}

Blocking semiovals in PG (2, 7) and beyond

(2,53) is constructed, as is a (4,11)-set of size 3189 in

Subregular Spreads of Hermitian Unitals

\mathcal{P}\mathcal{G}

Subregular Spreads of PG (5, 2 e )

(2,73).