New upper bounds on the smallest size of a complete arc in the plane PG(2, q) are obtained. New upper bounds on the smallest size of the complete cap in the space PG(n, q) are given for n = 3 and 25 ≤ q ≤ 97, q odd; n = 4 and q = 7, 8, 11, 13, 17; n = 5 and q = 5, 7, 8, 9; n = 6 and q = 4, 8. The bounds are obtained by computer search for new small complete arcs and caps. New upper bounds on the largest size of a complete cap in PG(n, q) are given. Many new sizes of complete arcs and caps are obtained.
On sizes of complete caps in projective spaces PG(n, q) and arcs in planes PG(2, q)
FAINA, Giorgio;MARCUGINI, Stefano;PAMBIANCO, Fernanda;
2009
Abstract
New upper bounds on the smallest size of a complete arc in the plane PG(2, q) are obtained. New upper bounds on the smallest size of the complete cap in the space PG(n, q) are given for n = 3 and 25 ≤ q ≤ 97, q odd; n = 4 and q = 7, 8, 11, 13, 17; n = 5 and q = 5, 7, 8, 9; n = 6 and q = 4, 8. The bounds are obtained by computer search for new small complete arcs and caps. New upper bounds on the largest size of a complete cap in PG(n, q) are given. Many new sizes of complete arcs and caps are obtained.File in questo prodotto:
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