Plane (s,3)-Arcs in PG(2,b)

(s, r)-caps are sets of s points in some space such that not more than r points are collinear. In this terminology normal s-caps are (s, 2)-caps. (s, r)-caps in the projective plane PG(2, b) over Fb are also known as plane (s, r)-arcs. (s, 3)-arcs in PG(2, b) correspond directly to linear [s, 3, s−3]-codes over Fb.

In [1] the following (s, 3)-arcs in PG(2, b) are shown to exist:

bsResulting code
39[9, 3, 6]-code over F3
49[9, 3, 6]-code over F4
511[11, 3, 8]-code over F5
715[15, 3, 12]-code over F7
815[15, 3, 12]-code over F8
917[17, 3, 14]-code over F9
1121[21, 3, 18]-code over F11
1323[23, 3, 20]-code over F13

References

[1]Simeon Ball.
On Sets of Points in Finite Planes.
PhD thesis, University of Sussex, U.K., 1994.

Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Plane (s,3)-Arcs in PG(2,b).” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CAMDSCodeN3.html

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