Conic blocking sets in Desarguesian projective planes

Define a conic blocking set to be a set of lines in a Desarguesian projective plane such that all conics meet these lines. Conic blocking sets can be used in determining if a collection of planes in projective three-space forms a flock of a quadratic cone. We discuss trivial conic blocking sets and conic blocking sets in planes of small order. We provide a construction for conic blocking sets in planes of non-prime order, and we make additional comments about the structure of these conic blocking sets in certain planes of even order.