Arne Botteldoorn

We obtain, by computer, a full classification up to equivalence of all minimal blocking sets with a nontrivial automorphism group in the Desarguesian projective plane of order 11. We list the resulting numbers of sets according to their size and the order of their automorphism group. For the minimal blocking sets with the larger automorphism groups, explicit descriptions are given. We also give a list of all blocking semiovals among the results. In contrast to similar work on the planes of smaller order, only those blocking sets were generated that have an automorphism group of size , as the number of minimal blocking sets with a trivial group is estimated to be infeasibly large. New algorithms had to be devised to obtain these results because simply generating all sets and filtering out those with a nontrivial automorphism group was totally impractical.

A full classification (up to equivalence) of all minimal blocking sets in PG(2, 9) 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 (geometric) descriptions are given. Some of these results can also be generalised to Desarguesian projective planes of higher order. We also give a complete list of all blocking semiovals in PG(2, 9) (up to equivalence). Mathematics Subject Classification (2020). 51E21, 51-04.