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 ℤ₃ 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: 2024-09-05. http://mint.sbg.ac.at/desc_CBoundB3M5Cap.html