A Result by Edel, Storme, and Sziklai

Let m₂(u, b) denote the size of the largest caps in the projective space PG(u, b) and m₂ʹ(u, b) the size of the second largest complete caps in PG(u, b). In [1] it is shown that m₂(4, 5) ≤ 88 and m₂(4, 7) ≤ 238. The results are obtained using computer searches for caps, based on knowledge about m₂ʹ(u−1, b).

Therefore, for every linear orthogonal array OA(5⁵, s, ℤ₅, 3) / linear [s, s−5, 4]-code over ℤ₅ we must have s ≤ 88 and for every linear OA(7⁵, s, ℤ₇, 3) / linear [s, s−5, 4]-code over ℤ₇ we must have s ≤ 238.

References

[1]	Yves Edel, Leo Storme, and Peter Sziklai. New upper bounds for the sizes of caps in PG(N, 5) and PG(N, 7). Journal of Combinatorial Mathematics and Combinatorial Computing, 60:7–32, 2007.

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. “A Result by Edel, Storme, and Sziklai.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_CBoundB57M5Cap.html