It has been shown that (t,m,s)-nets in base b can be characterized by combinatorial objects known as generalized orthogonal arrays. In this paper, a new construction for generalized orthogonal arrays leads to new (t,m,s)-nets in base q, q a prime power. The basic building block for the construction is an array of elements over Fq in which certain collections of rows are linearly independent. It is shown that if there exists an [n,n-m,d] q-ary code with $d\ge 6+2p$, where $p\ge 0$ is an integer, then there exists a (t,m,s)-net in base q with $t=m-(4+2p)$ and $s= \lfloor \frac{n-1}{1+p} \rfloor$.

A sharp lower bound on the covering radius of a linear, binary code is given in terms of the covering radius of any subcode of index two. An upper bound on the norm of a code is then derived. These results hold for all linear codes over GF(2).