A cap set in projective or affine geometry over a finite field is a set of points no three of which are collinear. In this paper we construct complete cap sets with sizes 274 432, 13 991 936, and 30 294 016 in affine geometries AG (16, 3), AG (21, 3), and AG (22, 3), respectively.
Karapetyan et al. (Mon,) studied this question.