Sporadic Bounds on the Size of Affine Caps

Let C_u(b) denote the size of the largest caps in the affine space AG(u, b). Then the following special values of C_u(b) are known:

Over F₃

• C₅(3) = 45 according to [1].

• C₆(3) = 112 according to [2].

Over F₄

• C₄(4) = 40 according to [3].

References

[1]	Yves Edel, S. Ferret, Ivan N. Landgev, and Leo Storme. The classification of the largest caps in AG(5, 3). Journal of Combinatorial Theory, Series A, 99(1):95–110, July 2002. doi:10.1006/jcta.2002.3261
[2]	Aaron Potechin. Maximal caps in AG(6, 3). Designs, Codes and Cryptography, 46(3):243–259, March 2008. doi:10.1007/s10623-007-9132-z
[3]	Yves Edel and Jürgen Bierbrauer. The largest cap in AG(4, 4) and its uniqueness. Designs, Codes and Cryptography, 29(1–2):99–104, May 2003. doi:10.1023/A:1024144223076

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. “Sporadic Bounds on the Size of Affine Caps.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_ABoundOther.html