  The second author recently suggested to identify the generating matrices of a
digital $(t,m,s)$-net over the finite field $F_q$ with an $s \times m$ matrix
$C$ over $F_{q^m}$. More exactly, the entries of $C$ are determined by
interpreting the rows of the generating matrices as elements of $F_{q^m}$. This
paper introduces so-called Vandermonde nets, which correspond to
Vandermonde-type matrices $C$, and discusses the quality parameter and the
discrepancy of such nets. The methods that have been successfully used for the
investigation of polynomial lattice point sets and hyperplane nets are applied
to this new class of digital nets. In this way, existence results for small
quality parameters and good discrepancy bounds are obtained. Furthermore, a
first step towards component-by-component constructions is made. A novelty of
this new class of nets is that explicit constructions of Vandermonde nets over
$F_q$ in dimensions $s \le q+1$ with best possible quality parameter can be
given. So far, good explicit constructions of the competing polynomial lattice
point sets are known only in dimensions $s \le 2$.
