Oval (Conic) Blocking Sets

Problem: To characterize the minimal sets of points in a plane with the property that every conic (odd characteristic) or oval/hyperoval (even characteristic) of the plane meets the set in at least one point.

First Cited: Cherowitzo, W., "Monomial Flocks of Monomial Cones in Even Characteristic".

Activity: Currently being worked on by Leanne Holder (graduate student, thesis topic).

Partial Results:

  1. In a plane of order q, the set of points on more than q + 1 - [(q+2)/2] concurrent lines is trivially an oval blocking set.
  2. For planes of small order (q = 2, 3, 4) all oval blocking sets can easily be determined.
  3. There exist several examples (given in these web pages) of non-trivial oval blocking sets.


Open Problems