  Following (Shevtsova, 2010) we introduce detailed classification of the
asymptotically exact constants in natural estimates of the rate of convergence
in the Lindeberg central limit theorem, namely in Esseen's, Rozovskii's, and
Wang-Ahmad's inequalities and their structural improvements obtained in our
previous works. The above inequalities involve algebraic truncated third-order
moments and the classical Lindeberg fraction and assume finiteness only the
second-order moments of random summands. We present lower bounds for the
introduced asymptotically exact constants as well as for the universal and for
the most optimistic constants which turn to be not far from the upper ones.
