A Problem Concerning Nonincident Points and Lines in Projective Planes

In this paper, we study the problem of finding the largest possible set of s points and s lines in a projective plane of order q, such that that none of the s points lie on any of the s lines. We prove that s <= 1+(q+1)(\sqrt{q}-1). We also show that equality can be attained in this bound whenever q is an even power of two.