  We consider the corner avoiding property of $s$-dimensional $\boldsymbol
\beta$-adic Halton sequences. After extending this class of point sequences in
an intuitive way, we show that the hyperbolic distance between each element of
the sequence and the closest corner of $[0,1)^s$ is
$\mathcal{O}\left(\frac{1}{N^{s/2+\epsilon}}\right)$, where $N$ denotes the
index of the element. In our proof we use tools from Diophantine analysis, more
precisely, we apply Schmidt's Subspace Theorem.
