New types of upper bounds for the smallest size t_2(2,q)of a complete arc in the projective plane PG(2,q) are proposed. In addition, our results allow us to conjecture that these estimates hold for all q. An algorithm FOP using any fixed order of points in PG(2,q) is proposed for constructing complete arcs. The algorithm is based on an intuitive postulate that PG(2,q)contains a sufficient number of relatively small complete arcs. It is shown that the type of order on the points of PG(2,q) is not relevant. 10 − 7 . In addition, our results allow us to conjecture that these estimates hold for all q . An algorithm FOP using any fixed order of points in PG (2 ,q ) is proposed for constructing com- plete arcs. The algorithm is based on an intuitive postulate that PG (2 ,q ) contains a sufficient number of relatively small complete arcs. It is shown that the type of order on the points of PG (2 ,q ) is not relevant.
New types of estimates for the smallest size of complete arcs in a finite Desarguesian projective plane
BARTOLI, DANIELE;FAINA, Giorgio;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2015
Abstract
New types of upper bounds for the smallest size t_2(2,q)of a complete arc in the projective plane PG(2,q) are proposed. In addition, our results allow us to conjecture that these estimates hold for all q. An algorithm FOP using any fixed order of points in PG(2,q) is proposed for constructing complete arcs. The algorithm is based on an intuitive postulate that PG(2,q)contains a sufficient number of relatively small complete arcs. It is shown that the type of order on the points of PG(2,q) is not relevant. 10 − 7 . In addition, our results allow us to conjecture that these estimates hold for all q . An algorithm FOP using any fixed order of points in PG (2 ,q ) is proposed for constructing com- plete arcs. The algorithm is based on an intuitive postulate that PG (2 ,q ) contains a sufficient number of relatively small complete arcs. It is shown that the type of order on the points of PG (2 ,q ) is not relevant.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
