A Aart Blokhuis

On the size of a blocking set in PG(2,p)

We show that the size of a non-trivial blocking set in the Desarguesian projective planePG(2,p), wherep is prime, is at least 3(p+1)/2. This settles a 25 year old conjecture of J. di Paola.

Maximal arcs in Desarguesian planes of odd order do not exist

Forq an odd prime power, and 1<n<q, the Desarguesian planePG(2,q) does not contain an(nq−q+n,n)-arc.

Some p -Ranks Related to Orthogonal Spaces

AbstractWe determine the p-rank of the incidence matrix of hyperplanes of PG(n, pe) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in

Lacunary polynomials, multiple blocking sets and Baer subplanes.

O_{10}^ + (2^e ),O_{10}^ + (3^e ),O_9 (5^e ),O_{12}^ + (5^e )

Permutations amongst the Dembowski-Ostrom polynomials

and

Proof of the prime power conjecture for projective planes of order

O_{12}^ + (7^e )