Let $\mathcal L$ be the space of unimodular (covolume one) lattices in $\mathbb R^d$. The $i$-th successive minima of $L\in \mathcal L$, denoted $\lambda_i(L)$ is the infimum of radius of the balls containing $i$-linearly independent vectors in $L$. For example, the first successive minima is the shortest nonzero vector in $L$ and the second successive minima is the second shortest vector in $L$ that is linearly independent of the first one.

I wonder if there are estimates/exact values for the following quantities for $1\le i \le d$:

$$A_i := \inf \{\lambda_i(L):L\in \Lambda\},$$

$$B_i := \sup \{\lambda_i(L):L\in \Lambda\}.$$

I know from Minkowski's second convex body theorem that two of them, namely $B_1 < \infty$ and $A_d >0$. In addition, $A_1=0$ via the following example $ \begin{bmatrix} e^{\frac{d-1}{d}t}I_{d-1} & 0 \\ 0 & e^{-\frac{t}{d}} \end{bmatrix} \mathbb Z^{d}$ as $t\to \infty$.

But what about the other $2d-3$ quantities? Are there ways to see they values? I suspect they are mostly either zero or infinite but can't rigorously see their specific values. Also I haven't found this discussed in any books in geometry of numbers or Diophantine approximations.