  A brief review of the results for the total cross section \sigma^{\nu N} of
ultrahigh-energy neutrino deep inelastic scattering on isoscalar nuclear
targets is presented. These results are based on simple approximations for
\sigma^{\nu N} and are compared with the experimental data of the IceCube
Collaboration. The total cross section \sigma^{\nu N} is proportional to the
structure function F_2^{\nu N}(M_V^2/s,M_V^2), where M_V is the intermediate
boson mass and s is square of the energy of the center of mass. The coefficient
in the front of F_2^{\nu N}(M_V^2/s,M_V^2) depends on the asymptotic behavior
of F_2^{\nu N} at low values of x. It contains an additional term \sim \ln{s}
if F_2^{\nu N} is scaled by the power \ln(1/x). Therefore, the asymptotic
behavior of F_2^{\nu N}\propto\ln^2(1/x) for small x often assumed in the
literature already leads to violation of the Froissart bound for \sigma^{\nu
N}.
