Small complete caps in \(PG(r,q)\), \(r\geq 3\)
A \(k\)-cap in \(PG(r,q)\), is a set of \(k\) points such that no three of them are collinear and, a \(k\)-cap is complete if it is maximal with respect to set-theoretic inclusion. Determining the largest and the smallest size of a complete cap of \(PG(r,q)\) seems to be a very hard problem. The authors, after surveying the known results on the minimal size of a complete cap of \(PG(r,q)\), give some new examples of complete caps in \(PG(3,q)\) and \(PG(4,q)\), which are, for particular values of \(q\), smaller than the caps so far constructed.
scientific article; zbMATH DE number 1110063
scientific article