  We perform self-consistent quantum transport calculations in open quantum
dots taking into account the effect of electron interaction. We demonstrative
that in the regime of the ultralow temperatures $2\pi k_BT\lesssim\Delta$
($\Delta $ being the mean level spacing), the electron interaction strongly
affects the conductance oscillations and their statistics leading to a drastic
deviation from the corresponding predictions for noninteracting electrons. In
particular, it causes smearing of conductance oscillations, which is similar to
the effect of temperature or inelastic scattering. For $2\pi k_BT\gtrsim\Delta$
the influence of electron interaction on the conductance becomes strongly
diminished. Our calculations (that are free from phenomenological parameters of
the theory) are in good quantitative agreement with the observed ultralow
temperature statistics (Huibers \textit{et al.}, Phys. Rev. Lett. \textbf{81},
1917 (1998)). Our findings question a conventional interpretation of the
ultralow temperature saturation of the coherence time in open dots which is
based on the noninteracting theories where the electron interaction is
neglected and the agrement with the experiment is achieved by introducing
additional phenomenological channels of dephasing.
