  Let $(\mathcal{X},\rho)$ be a metric space and $\lambda$ be a Borel measure
on this space defined on the $\sigma$-algebra generated by open subsets of
$\mathcal{X}$; this measure $\lambda$ defines volumes of Borel subsets of
$\mathcal{X}$. The principal case is where $\mathcal{X} = \mathbb{R}^d$, $\rho
$ is the Euclidean metric, and $\lambda$ is the Lebesgue measure. In this
article, we are not going to pay much attention to the case of small dimensions
$d$ as the problem of construction of good covering schemes for small $d$ can
be attacked by the brute-force optimization algorithms. On the contrary, for
medium or large dimensions (say, $d\geq 10$), there is little chance of getting
anything sensible without understanding the main issues related to construction
of efficient covering designs.
