41 Is the Largest Size of a Cap in PG(4, 4)

It is shown in [1] that a cap in the projective space PG(4, 4) cannot have more than 41 points. Therefore, for every linear orthogonal array OA(4⁵, s,F₄, 3) / linear [s, s−5, 4]-code over F₄ we must have s ≤ 41.

A cap/code with these parameters actually exists.

References

[1]	Yves Edel and Jürgen Bierbrauer. 41 is the largest size of a cap in PG(4, 4). Designs, Codes and Cryptography, 16(2):151–160, February 1999. doi:10.1023/A:1008389013117

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. “41 Is the Largest Size of a Cap in PG(4, 4).” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_CBoundB4M5Cap.html