This is an announcement for the paper "Tight embedding of subspaces of $L_p$ in $\ell_p^n$ for even $p$" by Gideon Schechtman. Abstract: Using a recent result of Batson, Spielman and Srivastava, We obtain a tight estimate on the dimension of $\ell_p^n$, $p$ an even integer, needed to almost isometrically contain all $k$-dimensional subspaces of $L_p$. Archive classification: math.FA Submitted from: gideon@weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.1061 or http://arXiv.org/abs/1009.1061