A Construction for (t,m,s)-nets in Base q

Abstract

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 $s= \lfloor \frac{n-1}{1+p} \rfloor$.