In this paper it has been verified, by a computer-based proof, that the smallest size of a complete arc is 12 in PG(2,27) and 13 in PG(2,29). Also the spectrum of the sizes of the complete arcs in PG(2,27) has been found. The classification of the smallest complete arcs of PG(2,27) is given: there are seven non-equivalent 12-arcs and for each of them the automorphism group and some geometrical properties are presented. Some examples of complete 13-arcs of PG(2,29) are also described.
Minimal complete arcs in PG(2,q), q<=29
MARCUGINI, Stefano;MILANI, Alfredo;PAMBIANCO, Fernanda
2003
Abstract
In this paper it has been verified, by a computer-based proof, that the smallest size of a complete arc is 12 in PG(2,27) and 13 in PG(2,29). Also the spectrum of the sizes of the complete arcs in PG(2,27) has been found. The classification of the smallest complete arcs of PG(2,27) is given: there are seven non-equivalent 12-arcs and for each of them the automorphism group and some geometrical properties are presented. Some examples of complete 13-arcs of PG(2,29) are also described.File in questo prodotto:
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