Geodesic
A lower bound for the convergence rate in the central limit theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 3, pp. 565-569 
V. K. Matskyavichyus. A lower bound for the convergence rate in the central limit theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 3, pp. 565-569. http://geodesic.mathdoc.fr/item/TVP_1983_28_3_a10/
@article{TVP_1983_28_3_a10,
     author = {V. K. Matskyavichyus},
     title = {A~lower bound for the convergence rate in the central limit theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {565--569},
     year = {1983},
     volume = {28},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_3_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For every sequence of nonnegative numbers $\varphi(n)\to 0$, $n\to\infty$ there exists a sequence of independent identically distributed random variables $X_1,X_2,\dots$ such that $\mathbf EX_1=0$, $\mathbf DX_1=1$ and for $n\ge n1$ $$ \sup_x|\mathbf P\{n^{-1/2}(X_1+\dots+X_n)<x\}-\Phi(x)|\ge\varphi(n). $$ The distribution of $X_1$ has the form $$ \mathbf P\{X_1<x\}=\sum_{k=1}^\infty\lambda_k\Phi(x/\sigma_k); $$ $\lambda_k$, $\sigma_k$ and $n_1$ are explicit functions of $\{\varphi(n)\}_{n=1}^\infty$.