  Node line (NL) band-touchings protected by mirror symmetry (named as $m$-NL),
the product of inversion and time reversal symmetry $\mathcal{S=PT}$ ($s$-NL),
or nonsymmorphic symmetry are nontrivial topological objects of topological
semimetals (SMs) in the Brillouin Zone (BZ). In this work, we screened the
family of MgSrSi-type crystals using first principles calculations, and
discovered that more than 70 members are NLSMs. A new type of multi-loop
structure was found in AsRhTi that a $s$-NL touches robustly with a $m$-NL at
some "nexus point", and in the meanwhile a second $m$-NL crosses with the
$s$-NL to form a Hopf-link. Unlike the previously proposed Hopf-link formed by
two $s$-NLs or two $m$-NLs, a Hopf-link formed by a $s$-NL and a $m$-NL
requires a minimal three-band model to characterize its essential electronic
structure. The associated topological surface states on different surfaces of
AsRhTi crystal were also obtained. Even more complicated and exotic multi-loop
structure of NLs were predicted in AsFeNa and PNiNb. Our work may shed light on
search for exotic multi-loop NLSMs in real materials.
