On maximal t-linearly independent sets

Consider a finite t + r ? 1 dimensional projective space PG(t + r ? 1, s) over a Galois field GF(s) of order s = ?^h, where ? and h are positive integers and ? is the prime characteristic of the field. A collection of k points in PG (t + r ? 1, s) constitutes an L(t, k)-set if no t of them are linearly dependent. An L(t, k)-set is maximal if there exists no other L(t, k′)-set with k′ > k. The largest k for which an L(t, k)-set exists is denoted by M_t(t + r, s). K. A. Bush 3] established that M_t(t, s) = t + 1 for t ? s. The purpose of this paper is to generalize this result and study M_t(t + r, s) for t, r, and s in certain relationships.