In the projective spaces PG(3, q), more than 370 new small complete caps are obtained for q < 3109, q prime. This implies new upper bounds on the smallest size t_2(3, q) of a complete cap in PG(3, q). From the new bounds it follows that the relation t_2(3, q) < 6q holds for q in R, where R is a set of 400 prime value in the interval [3, 3109]. The new upper bounds are obtained by finding new small complete caps in PG(3, q) with the help of a computer search using FOP (Fixed Order of Points) algorithm.
New upper bounds on the smallest size of a complete cap in the space PG(3, q)
BARTOLI, DANIELE;FAINA, Giorgio;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2013
Abstract
In the projective spaces PG(3, q), more than 370 new small complete caps are obtained for q < 3109, q prime. This implies new upper bounds on the smallest size t_2(3, q) of a complete cap in PG(3, q). From the new bounds it follows that the relation t_2(3, q) < 6q holds for q in R, where R is a set of 400 prime value in the interval [3, 3109]. The new upper bounds are obtained by finding new small complete caps in PG(3, q) with the help of a computer search using FOP (Fixed Order of Points) algorithm.File in questo prodotto:
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