Classification of the smallest minimal 1-saturating sets in

In this work we summarize some recent results to be included in a forthcoming paper [D. Bartoli, S. Marcugini, A. Milani and F. Pambianco, On the minimum size of complete arcs and minimal saturating sets in P G ( 2 , q ) , q small, preprint.]. The classification of all the minimal 1-saturating sets in P G ( 2 , 9 ) and P G ( 2 , 11 ) and the classification of minimal 1-saturating sets of the smallest size in P G ( 2 , q ) , 16 ⩽ q ⩽ 23 , are given. These results have been found using a computer-based exhaustive search that exploits projective equivalence properties.