  We present a simple formula for the total cross section sigma^{nu N} of
neutral- and charged-current deep-inelastic scattering of ultrahigh-energy
neutrinos on isoscalar nuclear targets, which 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 the square of the center-of-mass energy. The coefficient in the front
of F_2^{nu N}(x, Q^2) depends on the asymptotic low-x behavior of F_2^{nu N}.
It contains an additional ln(s) term if F_2^{nu N} scales with a power of
ln(1/x). Hence, an asymptotic low-x behavior F_2^{nu N} propto ln^2(1/x), which
is frequently assumed in the literature, already leads to a violation of the
Froissart bound on sigma^{nu N}.
