  Bl\"omer and Seifert showed that $\mathsf{SIVP}_2$ is NP-hard to approximate
by giving a reduction from $\mathsf{CVP}_2$ to $\mathsf{SIVP}_2$ for constant
approximation factors as long as the $\mathsf{CVP}$ instance has a certain
property. In order to formally define this requirement on the $\mathsf{CVP}$
instance, we introduce a new computational problem called the Gap Closest
Vector Problem with Bounded Minima. We adapt the proof of Bl\"omer and Seifert
to show a reduction from the Gap Closest Vector Problem with Bounded Minima to
$\mathsf{SIVP}$ for any $\ell_p$ norm for some constant approximation factor
greater than $1$.
  In a recent result, Bennett, Golovnev and Stephens-Davidowitz showed that
under Gap-ETH, there is no $2^{o(n)}$-time algorithm for approximating
$\mathsf{CVP}_p$ up to some constant factor $\gamma \geq 1$ for any $1 \leq p
\leq \infty$. We observe that the reduction in their paper can be viewed as a
reduction from $\mathsf{Gap3SAT}$ to the Gap Closest Vector Problem with
Bounded Minima. This, together with the above mentioned reduction, implies
that, under Gap-ETH, there is no $2^{o(n)}$-time algorithm for approximating
$\mathsf{SIVP}_p$ up to some constant factor $\gamma \geq 1$ for any $1 \leq p
\leq \infty$.
