Complete Caps in Affine Geometry AG(n, 3)

Abstract

We consider the problem of constructing complete caps in affine geometry AG(n, 3) of dimension n over the field F₃ of order three. We will take the elements of F₃ to be 0, 1 and 2. A cap is a set of points, no three of which are collinear. Using the concept of P_n - set, we give two new methods for constructing complete caps in affine geometry AG(n, 3). These methods lead to some new upper and lower bounds on the possible minimal and maximal cardinality of complete caps in affine geometry AG(n, 3).