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Let V ⊂ Z be two subspaces of a Banach space X. We define the set of generalized projections by ${}_V(X,Z):={P\in (X,Z):P|}_V=id$. Now let X = c₀ or $l_{\infty }^m$, Z:= kerf for some f ∈ X* and $V:=Z\cap l{ⁿ}_{\infty }$ (n < m). The main goal of this paper is to discuss existence, uniqueness and strong uniqueness of a minimal generalized projection in this case. Also formulas for the relative generalized projection constant and the strong uniqueness constant will be given (cf. J. Blatter and E. W. Cheney [Ann. Mat. Pura Appl. 101 (1974), 215-227] and G. Lewicki...