A class of complete \(k\)-caps of small cardinality in projective spaces over fields of characteristic three (Q1808813)

A \(k\)-cap in a projective space is a set of \(k\) points, no three of which are collinear. The \(k\)-cap is complete if it is not included in a \(k+1\)-cap. The author studies \(k\)-caps in \(PG(3,q)\), where \(q=3^n\), \(n>1\). He starts with the irreducible quadratic \(x^2_1-ax^2_2 +x^2_3-2 x_3x_0=0\). He gives a construction for a class of \(k\)-caps in this space with \(k=(q^2+4)/3\).