  In this paper we study tractability properties of the weighted star
discrepancy with general coefficients of centered regular grids with different
mesh-sizes. We give exact characterizations of the weight sequences
$(\gamma_j)_{j \ge 1}$ such that the regular grid with different mesh-sizes
achieves weak, uniform weak, quasi polynomial, polynomial or strong polynomial
tractability for the $\boldsymbol{\gamma}$-weighted star discrepancy. For
example, a necessary and sufficient condition such that the regular grid with
different mesh-sizes achieves weak tractability for the
$\boldsymbol{\gamma}$-weighted star discrepancy is $\lim_{j \rightarrow
\infty}j \gamma_j=0$.
