Small proper double blocking sets in Galois planes of prime order

A proper double blocking set in PG(2, p) is a set B of points such that 2 |B ∩ 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. © 2007 Elsevier B.V. All rights reserved.