This is an announcement for the paper "The asymptotic growth of the constants in the Bohnenblust-Hille inequality is optimal" by Diogo Diniz, G. A. Munoz-Fernandez, Daniel Pellegrino and J. B. Seoane-Sepulveda. Abstract: In this note we provide a family of constants, $C_{n}$, enjoying the Bohnenblust--Hille inequality and such that $\lim_{n\rightarrow\infty}C_{n}/C_{n-1}=1$, i.e., their asymptotic growth is the best possible. As a consequence, we also show that the optimal constants, $K_n$, in the Bohnenblust--Hille inequality have the best possible asymptotic behavior. Archive classification: math.FA Submitted from: dmpellegrino@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1108.1550 or http://arXiv.org/abs/1108.1550