On blocking sets of conics
by
Leanne D. Holder
Univeristy of Colorado at Denver

A conic blocking set (CBS) is a set of lines in PG(2, q) with the property that every conic of the plane intersects at least one of the lines. A CBS is irreducible provided it contains no smaller CBS. The study of these sets is in its infancy, and we report our preliminary findings.

In this talk, the special case where the lines of the CBS are concurrent is examined. We provide constructions for CBSs in both odd and even characteristic; and in the particular case where q is even, a construction for an irreducible conic blocking set is provided. Some of these constructions rely on Thas' results related to the theory of flocks of quadratic cones.

Finally, we report on the progress made in obtaining bounds for the sizes of minimal conic blocking sets of this type. An efficient algorithm is developed by dualizing the problem and incorporating optimization techniques. The results of these computers searches are presented for planes of order less than 200 for odd characteristic and in planes of order less than 1024 for even characteristic.

Date received: February 23, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagg-09.