This is an announcement for the paper "On near-optimal admissible meshes" by Alexander Brudnyi. Abstract: We show that every compact subset of $\mathbb C^n$ admits a near-optimal admissible mesh. We apply this result to study geometric properties of Banach spaces of traces of real polynomials on $\mathbb R^n$ to compact subsets equipped with supremum norms. Archive classification: math.FA Mathematics Subject Classification: 41A10, 41A17, 65D05 Remarks: 6 pages Submitted from: albru@math.ucalgary.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2303 or http://arXiv.org/abs/1402.2303