a classical result of siegel asserts that the (2,3,7)-triangle group attains the smallest covolume among lattices of $\rm{sl}_2(\mathbb{r})$. in general, given a semisimple lie group $g$ over some local field $f$, one may ask which lattices in $g$ attain the smallest covolume. a complete answer to this question seems out of reach at the moment; nevertheless, many steps have been made in the last decades. inspired by siegel's result, lubotzky determined that a lattice of minimal covolume in $\mathrm{sl}_2(f)$ with $f=\mathbb{f}_q(\!(t)\!)\) is given by the so-called the characteristic $p$ modular group $\mathrm{sl}_2(\mathbb{f}_q[1/t])$. he noted that, in contrast with siegel's lattice, the quotient by $\mathrm{sl}_2(\mathbb{f}_q[1/t])$ was not compact, and asked what the typical situation should be: for a semisimple lie group over a local field, is a lattice of minimal covolume a cocompact or nonuniform lattice? in the talk, we will review some of the known results, and then discuss the case of $\mathrm{sl}_n(\mathbb{r})$ for $n > 2$. it turns out that, up to automorphism, the unique lattice of minimal covolume in $\mathrm{sl}_n(\mathbb{r})$ is $\mathrm{sl}_n(\mathbb{z})$. in particular, it is not uniform, giving an answer to lubotzky's question in this case.