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 5 we must have s ≤ 88 and for every linear OA(75, s, ℤ7, 3) / linear [s, s−5, 4]-code over 7 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: 2008-04-04. http://mint.sbg.ac.at/desc_CBoundB57M5Cap.html

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