Complete caps in projective spaces PG\((n,q)\) (Q1882440)

A \(k\)-cap of the projective space \(PG(n,q)\) is a set of \(k\) points, no three collinear. A complete \(k\)-cap of \(PG(n,q)\) is a \(k\)-cap which is not contained in any \((k+1)\)-cap. There exist several bounds on the size of complete caps of a projective space; however, the complete spectrum of values of \(k\) for which a \(k\)-cap of \(PG(n,q)\) exists is not known. The results of a randomised computer search for caps are presented in this paper and, in particular, new possible sizes of caps are determined in several cases.