  We consider convex optimization problems with the objective function having
Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new
tensor method, which closes the gap between the lower
$O\left(\varepsilon^{-\frac{2}{3p+1}} \right)$ and upper
$O\left(\varepsilon^{-\frac{1}{p+1}} \right)$ iteration complexity bounds for
this class of optimization problems.
  We also consider uniformly convex functions, and show how the proposed method
can be accelerated under this additional assumption. Moreover, we introduce a
$p$-th order condition number which naturally arises in the complexity analysis
of tensor methods under this assumption.
  Finally, we make a numerical study of the proposed optimal method and show
that in practice it is faster than the best known accelerated tensor method. We
also compare the performance of tensor methods for $p=2$ and $p=3$ and show
that the 3rd-order method is superior to the 2nd-order method in practice.
