Some projections and their properties in the space $l^{mn}_{\infty }$ ($m\geq 2$, $n\geq 3$)

The paper considers projections of the space $l_\infty ^{mn}$ onto a certain class of subspaces of codimension $m$, which are formed by using hyperplanes of $l_\infty ^{mn}$. For them we find relative projection constants and constants of strong uniqueness. In some of the cases under consideration, the relative projection constant is equal to $1$, and in others it is greater than $1$. The maximum values of the constants of strong uniqueness are calculated for the projections with unit norm.