Abstract
In this paper we introduce digital nets over finite abelian groups which contain digital nets over finite fields and certain rings as a special case. We prove a MacWilliams-type identity for such digital nets. This identity can be used to compute the strict $t$-value of a digital net over finite abelian groups. If the digital net has $N$ points in the $s$-dimensional unit cube $[0,1)^s$, then the $t$-value can be computed in $\mathcal{O}(N s \log N)$ operations and the weight enumerator polynomial can be computed in $\mathcal{O}(N s (\log N)^2)$ operations, where operations mean arithmetic of integers. By precomputing some values the number of operations of computing the weight enumerator polynomial can be reduced further.
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