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A000509
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Size of second largest n-arc in PG(2,q), where q runs through the primes and prime powers >= 7.
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1
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6, 6, 8, 10, 12, 13, 14, 14, 17, 21, 22, 24
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sufficient data to extend this through q = 2333 is in Davydov. New upper bounds on the smallest size of a complete arc in the projective plane PG(2,q) are obtained for 841 <= q <= 2333. The bounds are obtained by computer search using a randomized greedy algorithm. Also new sizes of complete arcs are presented. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 18 2010]
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REFERENCES
| J. W. P. Hirschfeld, Complete arcs, Discr. Math., 174 (1997), 177-184.
J. W. P. Hirschfeld and L. Storme, The packing problem in statistics, coding theory and finite projective spaces, J. Statist. Plann. Inference 72 (1998), no. 1-2, 355-380.
G. Keri, Types of superregular matrices and the number of n-arcs and complete n-arcs in PG(r,q), Journal of Combinatorial Designs, Vol. 14 (2006), pp. 363-390.
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LINKS
| Alexander A. Davydov, Giorgio Faina, Stefano Marcugini, Fernanda Pambianco, New sizes of complete arcs in PG(2,q), April 16, 2010. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 18 2010]
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EXAMPLE
| m'(31)=22 because there are no complete n-arcs in PG(2,31) for 23<=n<=31
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CROSSREFS
| Cf. A000510.
Cf. A000961.
Sequence in context: A201578 A195707 A175217 * A141218 A160257 A183042
Adjacent sequences: A000506 A000507 A000508 * A000510 A000511 A000512
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KEYWORD
| nonn,hard,nice
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AUTHOR
| J. W. P. Hirschfeld [ jwph(AT)sussex.ac.uk ]
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EXTENSIONS
| Definition clarified by G. Keri (keri(AT)sztaki.hu), Jan 03 2008
New arXiv paper has data sufficient for a b-list. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 18 2010]
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