arbitrary cover of $L$ in $\mathbb{R}^s$. The *spacing* $d({\mathcal{H}_ C})$ of ${\mathcal{H}_ C}$ will denote the minimal distance between adjacent hyperplanes in this family, $
d({\mathcal{H}_ C}) = \inf \left\{  d({H_{c}}, {H_{d}}) : c\neq d, \
        c,d  \in C \right\}.
$

We define *the spectral test* of $L$ as the number $$\sigma (L) := \sup \left\{ d({\mathcal{H}_ C}): {\mathcal{H}_ C}\text{ is a
        cover of } L \right\}.$$

The following theorem is well known in the theory of pseudorandom number generation (see [@Fis96a; @Hel98a; @Knu98a; @Lee95c]). Computational aspects are discussed in [@Lec99a].

Let $L$ be an $s$-dimensional lattice. Then $$\label{eqn:classicalsigma}
\sigma(L) = 1/\min \{||{\ensuremath{\mathbf g}}||_2: {\ensuremath{\mathbf g}}\in L^\bot, {\ensuremath{\mathbf g}}\text{ primitive }  \},$$ where $||{\ensuremath{\mathbf g}}||_2 = (g_1+ \dots + g_s)^{1/2}$ is the Euclidean norm on ${\ensuremath{\mathbb{R}}}^s$.

In the field of quasi-Monte Carlo integration, similar concepts have been developed within the context of [*good lattice points*]{}.

\[def:GLP\] For a given integer $N\ge 2$ and for a given dimension $s\ge2$, we call an integer point $\mathbf{a} = (a_1, \ldots, a_s)\in$ $\mathbb{Z}^s$, $\gcd(a_i, N)=1$, $1\le i\le s$, a *good lattice point* modulo $N$ if the finite sequence $$\label{eqn:GLPa}
\omega_\mathbf{a} = \left( \left\{ \frac{n}{N}\;
        \mathbf{a} \right\} \right)_{n=0}^ {N-1}$$ is “very uniformly” distributed in $[0,1)^s$ 