Meshes that trap random subspaces

In our recent work [30, 33] we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved results related to performance of a polynomial l1-optimization technique when used for solving such systems. As one of the tools we used a probabilistic result of Gordon [18]. In this paper we revisit this classic result in its core form and show how it can be reused to in a sense prove its own optimality.