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A365198
Smallest k such that there exists a complete k-arc on the projective plane over GF(q), where q = A246655(n) is the n-th prime power > 1.
0
4, 4, 6, 6, 6, 6, 6, 7, 8, 9, 10, 10, 10, 12, 12, 13, 14, 14
OFFSET
1,1
COMMENTS
A k-arc is a set of k points in PG(2,q) (the projective plane over GF(q)) such that no three are collinear. A complete k-arc is a k-arc which is not contained in any (k+1)-arc.
REFERENCES
J. W. P. Hirschfeld, Projective geometries over finite fields, Second edition, Oxford Math. Monogr., The Clarendon Press, Oxford University Press, New York, 1998.
LINKS
D. Bartoli, G. Faina, S. Marcugini and F. Pambianco, On the minimum size of complete arcs and minimal saturating sets in projective planes, J. Geom. 104 (2013), no. 3, 409-419.
S. Marcugini, A. Milani, and F. Pambianco, Minimal complete arcs in PG(2,q), q <= 32, arXiv:1005.3412 [math.CO], 2010.
B. Segre, Le geometrie di Galois, Ann. Mat. Pura Appl. (4) 48 (1959), 1-96.
FORMULA
a(n) > sqrt(2*A246655(n)) + 1 [Segre].
CROSSREFS
Cf. A365216.
Sequence in context: A121064 A213342 A019559 * A274636 A198697 A111657
KEYWORD
nonn,hard,more
AUTHOR
Robin Visser, Aug 26 2023
STATUS
approved