Zohar Karnin

For any $00$, we give an efficient

deterministic construction of a linear subspace $V \subseteq

\R^n$, of dimension $(1-\epsilon)n$ in which the $\ell_p$ and

$\ell_r$ norms are the same up to a multiplicative factor of

$\poly(\epsilon^{-1})$ (after the correct normalization). As a

corollary we get a deterministic compressed sensing algorithm

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