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On the existence and the nonexistence of some (k,n)-arcs in PG(2,37) | ||
| Journal of Basrah Researches (Sciences) | ||
| Article 1, Volume 39, Issue 2, 2013, Pages 40-48 PDF (0 K) | ||
| Author | ||
| Mohanad S. Khalid | ||
| Abstract | ||
| A (k,n)-arc is a set of k points of a projective plane such that some n, but no n+1 of them, are collinear. The maximum size of a (k,n)-arc in PG(2 q) is denoted by m_n (2,q). In this paper we proved that 666〖≤m〗_21 (2,37)≤741, 〖703≤m〗_22 (2,37)≤779, 739〖≤m〗_23 (2,37)≤817, 777〖≤m〗_24 (2,37)≤855, 816〖≤m〗_25 (2,37)≤893, 854〖≤m〗_26 (2,37)≤931, 894〖≤m〗_27 (2,37)≤969, 〖933≤m〗_28 (2,37)≤1007, 970〖≤m〗_29 (2,37)≤1045, m_30 (2,37)≤1083, m_31 (2,37)≤1121, m_32 (2,37)≤1159, m_33 (2,37)≤1197, m_34 (2,37)≤1235, m_35 (2,37)≤1273 and m_36 (2,37)≤1311. | ||
| Keywords | ||
| Projective spaces; arcs; blocking set | ||
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