A lower bound of the strongly unique minimal projection constant of lninfinity, n>=3

In this paper we give a lower bound for the strongly unique minimal projection (with norm one) constant (SUP-constant) onto some (n − k)-dimensional subspaces of l ∞ (n ≥ 3, 1 ≤ k ≤ n−1). By Proposition 1 of this paper, each k-dimensional Banach space with polytope unit ball with m (k − 1)-faces is isometrically isomorphic to a subspace of lk+m−1 ∞ . As such the aforementioned estimation can be applied to spaces other than l ∞. We also include a conjecture about the exact calculations of SUP-constants in particular settings.