Large caps in projective Galois spaces

coauthor Jürgen Bierbrauer

Chapter in Current research topics in Galois geometry Nova Science Publishers, 87-104, 2012,
Jan De Beule and Leo Storme Eds. To appear.


Abstract:

A cap in a projective or affine geometry over a finite field is a set of points no three of which are collinear. The most natural question to ask is:
What is the maximum size of a cap in the given space?
This is also known as the packing problem. In this paper we give an overview on the known results. Also new constructions are presented such as a construction of an 541-cap in PG(8,3) an 195-cap in AG(5,5) an 5069-cap in PG(8,5) and an 130951-cap in PG(11,5). Related topics as quantum caps and a problem in additive number theory are discussed.


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