Caps Completed Using a Computer Search

Constructions for caps in the projective space PG(u, b) with b > 2 are given in [1], with two extensions in [2]. Most of these caps are constructed by adding points to known caps until a complete cap is reached. Generator matrices for all these caps can be found at Yves Edel’s home page at http://www.mathi.uni-heidelberg.de/~yves/Matritzen/CAPs/CAPMatIndex.html.

The following caps are included:

Over the Field with Size b = 3

Dimension uSizeLargest affine sub-cap
7248236
8532476
912161068
1027442228
1164645232
121331210848

Over the Field with Size b = 4

Dimension uSizeLargest affine sub-cap
44040
821102008
949384692
101542314667

Over the Field with Size b = 5

Dimension uSizeLargest affine sub-cap
46665
5186176
847004510
91712416434

Over the Field with Size b = 7

Dimension uSizeLargest affine sub-cap
4132127
5434427
764726340
82155521144

Over the Field with Size b = 8

Dimension uSizeLargest affine sub-cap
4208208
5695694

Over the Field with Size b = 9

Dimension uSizeLargest affine sub-cap
4210210
4212209

Over the Field with Size b = 11

Dimension uSizeLargest affine sub-cap
4316311

Over the Field with Size b = 13

Dimension uSizeLargest affine sub-cap
4388387

Over the Field with Size b = 16

Dimension uSizeLargest affine sub-cap
4629628

Over the Field with Size b = 32

Dimension uSizeLargest affine sub-cap
431363136

References

[1]Yves Edel and Jürgen Bierbrauer.
Large caps in small spaces.
Designs, Codes and Cryptography, 23(2):197–212, July 2001.
doi:10.1023/A:1011216716700
[2]Yves Edel.
Extensions of generalized product caps.
Designs, Codes and Cryptography, 31(1):5–14, January 2004.
doi:10.1023/A:1027365901231

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. “Caps Completed Using a Computer Search.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CCapsCompletion.html

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