## Bound for Caps in PG(4, *b*)

Let *m*_{2}(*u*, *b*) denote the size of the largest caps in the projective space PG(*u*, *b*). Then, for all *b* ≥ 7, we have

*m*

_{2}(4,

*b*) ≤

*b*

^{3}–

*b*

^{2}+

The result for odd *b* is due to [1], the result for even *b* to [2] and [3]. See also [4, Table 4.3(i)].

### References

[1] | Adriano Barlotti. Some topics in finite geometrical structures. Mimeo Series 439, Institute of Statistics, Univ. of North Carolina, 1965. |

[2] | Jin-Ming Chao. On the size of a cap in PG( n, q) with q even and n ≥ 3.Geometriae Dedicata, 74(1):91–94, January 1999.doi:10.1023/A:1005095418152 |

[3] | James W. P. Hirschfeld and Joseph A. Thas. Linear independence in finite spaces. Geometriae Dedicata, 23(1):15–31, May 1987.doi:10.1007/BF00147388 |

[4] | 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. |

### 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. “Bound for Caps in PG(4, *b*).”
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