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Let $c&gt;\sqrt{2}$ and let $p$ be a prime number. J-M. Deshouillers and G. A. Freiman proved that a subset $\mathcal A$ of $\mathbb{Z}/p\mathbb{Z}$, with cardinality larger than $c\sqrt{p}$ and such that its subset sums do not cover $\mathbb{Z}/p\mathbb{Z}$ has an isomorphic image which is rather concentrated; more precisely, there exists $s$ prime to $p$ such that $$\sum_{a\in\mathcal A}\Vert\frac{as}{p}\Vert  1+Kp^{-1/2}.$$

A lower bound concerning subset sums which do not cover all the residues modulo $p$.