Name for this notion of "pair-wise reduced" basis?

Question

Let $\mathcal{B}=\{b_1,\ldots,b_n\}$ be a basis for a full-rank lattice $\Lambda\subset\mathbb{R}^n$. Say the basis is "pair-wise reduced" if for all $i\neq j$ $$ -\frac{1}{2}\leq\frac{\langle b_i,b_j\rangle}{\langle b_j,b_j\rangle}<\frac{1}{2}. $$ Is there a name for this sort of "pair-wise reduced" basis? Does it imply any nice properties, e.g. bounds on the shortest vector in $\Lambda$ in terms of $\mathcal{B}$? Any references or reasons why this isn't interesting are appreciated.