  We present electronic transport and magnetic properties of single crystals of
semimetallic half-Heusler phase LuPdBi, having theoretically predicted band
inversion requisite for nontrivial topological properties. The compound
exhibits superconductivity below a critical temperature $T_{\rm c}=1.8\,$K,
with a zero-temperature upper critical field $B_{\rm c2}\approx2.3\,$T.
Although superconducting state is clearly reflected in the electrical
resistivity and magnetic susceptibility data, no corresponding anomaly can be
seen in the specific heat. Temperature dependence of the electrical resistivity
suggests existence of two parallel conduction channels: metallic and
semiconducting, with the latter making negligible contribution at low
temperatures. The magnetoresistance is huge and clearly shows a weak
antilocalization effect in small magnetic fields. Above about 1.5 T, the
magnetoresistance becomes linear and does not saturate in fields up to 9 T. The
linear magnetoresistance is observed up to room temperature. Below 10 K, it is
accompanied by Shubnikov-de Haas oscillations. Their analysis reveals charge
carriers with effective mass of $0.06\,m_e$ and a Berry phase very close to
$\pi$, expected for Dirac-fermion surface states, thus corroborating
topological nature of the material.
