A Result by Gronchi and Heim

Let m2(u, b) denote the size of the largest caps in the projective space PG(u, b). In [1, Table 4.3(i)], the following upper bounds on m2(4, b) are listed:

These bounds are obtained by applying the ideas of Gronchi [2] to the results of Heim [3].


[1]James W. P. Hirschfeld and Leo Storme.
The packing problem in statistics, coding theory and finite projective spaces: Update 2001.
In Finite Geometries, volume 3 of Developments in Mathematics, pages 201–246. Kluwer Academic Publishers, 2001.
[2]Paolo Gronchi.
I blocking sets ed il packing problem.
Unione Matematica Italiana. Bollettino. A. Serie VII, 7(2):227–236, 1993.
[3]U. Heim.
On t-blocking sets in projective spaces, 1994.
Unpublished manuscript.


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 Gronchi and Heim.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_CBoundB91113M5Cap.html

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