  In this paper, we study quasi-Monte Carlo (QMC) rules for numerical
integration. J. Dick proved a Koksma-Hlawka type inequality for $\alpha$-smooth
integrands and gave an explicit construction of QMC rules achieving the optimal
rate of convergence in that function class. From this inequality, Matsumoto et
al. introduced Walsh figure of merit (WAFOM) $\mathrm{WAFOM}(P)$ for an
$\mathbb{F}_2$-digital net $P$ as a quickly computable quality criterion for
$P$ as a QMC point set. The key ingredient for obtaining WAFOM is the Dick
weight, a generalization of the Hamming weight and the
Niederreiter-Rosenbloom-Tsfasman (NRT) weight.
  We extend the notions of the Dick weight and WAFOM for digital nets over a
general finite abelian group $G$, and show that this version of WAFOM satisfies
Koksma-Hlawka type inequality when $G$ is cyclic. We give a MacWilliams-type
identity on the weight enumerator polynomials for the Dick weight, by which we
can compute the minimum Dick weight as well as WAFOM. We give a lower bound of
WAFOM of order $N^{-C'_G(\log N)/s}$ and an upper bound of lowest WAFOM of
order $N^{-C_G(\log N)/s}$ for given $(G,N,s)$ if $(\log N)/s$ is sufficiently
large, where $N$ is the cardinality of the point set $P$, $P$ is a quadrature
rule in $[0,1)^s$, and $C'_G$ and $C_G$ are constants depending only on the
cardinality of $G$. These bounds generalize the bounds given by Yoshiki and
others given for $G=\mathbb{F}_2$.
