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: 2008-04-04. http://mint.sbg.ac.at/desc_CBoundB4M5Cap.html

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