Small proper double blocking sets in Galois planes of prime order.

Discrete Mathematics 308 (2008), 4052-4056.

A proper double blocking set in PG(2,p) is a set B of points such that 2 <= |B n l| <= (p+1)-2 for each line l. The smallest known example of a proper double blocking set in PG(2,p) for large primes p is the disjoint union of two projective triangles of side (p+3)/2; the size of this set is 3p+3. For each prime p >= 11 such that p=3 (mod 4) we construct a proper double blocking set with 3p+1 points, and for each prime p >= 7 we construct a proper double blocking set with 3p+2 points.