This is an announcement for the paper "A note on the best constants for the Bohnenblust-Hille inequality" by Daniel Pellegrino. Abstract: In this note we show that a recent new proof of Bohnenblust-Hille inequality, due to Defant et al, combined with the better known constant for Littlewood 4/3 theorem and the optimal constants of Khinchin inequality, due to Haagerup, provide quite better estimates for the constants involved in the Bohnenblust-Hille inequality. For example, if $2\leq m\leq13,$ we show that the constants $C_{m}=2^{(m-1)/2}$ can be replaced by $2^{\frac{m^{2}+m-6}{4m}% }K_{G}^{2/m}$, which are substantially better than $C_{m}$ (here $K_{G}$ denotes the complex Grothendieck Archive classification: math.FA Remarks: 7 pages Submitted from: dmpellegrino@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2717 or http://arXiv.org/abs/1009.2717