  We provide an example for the generating matrix $A$ of a two-dimensional
lattice $\Gamma = A\mathbb{Z}^2$, such that the following holds: For any
sufficiently smooth and localized mother wavelet $\psi$, there is a constant
$\beta(A,\psi)>0$, such that $\beta\Gamma\cap (\mathbb{R}\times\mathbb{R}^+)$
is a set of stable sampling for the wavelet system generated by $\psi$, for all
$0<\beta\leq \beta(A,\psi)$. The result and choice of the generating matrix are
loosely inspired by the studies of low discrepancy sequences and uniform
distribution modulo $1$. In particular, we estimate the number of lattice
points contained in any axis parallel rectangle of fixed area. This estimate is
combined with a recent sampling result for continuous wavelet systems, obtained
via the oscillation method of general coorbit theory.
