20 Is the Largest Size of a Cap in PG(4, 3)

It is shown in [1] that a cap in the projective space PG(4, 3) cannot have more than 20 points. Caps attaining this size are therefore called Pellegrino caps.

It follows that every linear orthogonal array OA(35, s, ℤ3, 3) / linear [s, s−5, 4]-code over 3 must have s ≤ 20.

References

[1]Giuseppe Pellegrino.
Sul massimo ordine delle calotte in S4,3.
Le Matematiche (Catania), 25:149–157, 1971.

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. “20 Is the Largest Size of a Cap in PG(4, 3).” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CBoundB3M5Cap.html

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