Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better parameters. Namely, for $$\varepsilon=3.26\cdot 10^{-7}$$ , large $$k$$ and $$k^{2-\varepsilon} \le N\le k^{2+\varepsilon}$$ construct $$n \times N$$ RIP of order $$k = \Omega( n^{1/2+\varepsilon/4)}$$ .