# Definition

Let $\delta\in\left(\frac14,1\right)$. A basis$\left\{b_i\right\}_{i=1}^d$is $\delta$- LLL-reduced if it is size reduced and satisfy the Lovász condition, i.e.

$\delta\left\lVert b_i^*\right\rVert^2\leq\left\lVert b_{i+1}^*+\mu_{i+1,i}b_i^*\right\rVert^2$

This notion of reduction is most useful to use for fast algorithms as such a basis can be found in polynomial time (see LLL reduction).