Classification of minimal blocking sets in small Desarguesian projective planes

Abstract

A full classification (up to equivalence) of all minimal blocking sets in Desarguesian projective planes of order ≤ 8 was obtained by computer. The resulting numbers of minimal blocking sets are tabulated according to size of the set and order of the automorphism group. For the minimal blocking sets with the larger automorphism groups explicit descriptions are given. Some of these results can also be generalised to Desarguesian projective planes of higher order.

Classification of minimal blocking sets in PG(2,9)

“…Although we use essentially the same algorithm as in [7], the new implementation for the particular case of PG (2,9) turned out to be significantly faster. The earlier implementation represented points and lines by their coordinate triples and used a matrix representation for projectivities, while the most recent version represents the plane as a perfect difference set and uses a permutation group representation, employing Nauty [16] for isomorphism checks.…”