Kolmogorov widths of an intersection of anisotropic finite-dimensional balls: case $2\le q_j<\mathrm{\infty }$

Order estimates for the Kolmogorov $n$-widths of ${\cap }_{\alpha \in A}{\nu }_{\alpha }{B}_{\bar{p}}^{\bar{k}}$ in $l_{\bar{q}}^{\bar{k}}$ are obtained; here $\bar{q}=(q_1,\dots ,q_d)$, $2\le q_j<\mathrm{\infty }$, $j=1,\dots ,d$.