A combinatorial problem with applications to geometry

AbstractIn the construction of sets of orthogonal Latin hypercubes and in the study of finite projective geometries, the following question arises: Given an r-dimensional vector space over a finite field, what is the maximum number of vectors that can be found such that any r form a basis for the space? With the aid of combinatorial results arising from the study of hypercubes, in this paper we obtain results for (n − 1)-dimensional spaces over fields of n elements