Geodesic
Constants of Strong Uniqueness of Minimal Projections onto Hyperplanes in the Space $\ell _\infty ^n$ ($n\ge 3$)
Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 723-728.

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In this paper, we obtain the maximum values of the constants of strong uniqueness of minimal projections with nonunit norm on hyperplanes in the space $\ell _\infty ^n$ ($n\ge 3$). 
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V. V. Lokot'. Constants of Strong Uniqueness of Minimal Projections onto Hyperplanes in the Space  $\ell _\infty ^n$ ($n\ge 3$). Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 723-728. http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a10/

[1] Blatter J., Cheney E. W., “Minimal projections onto hyperplanes in sequence spaces”, Ann. Mat. Pura Appl., 101 (1974), 215–217 | DOI | MR

[2] Odinnec V. P., “On the uniqueness of minimal projections in $\ell_\infty^n$ ($n\ge3$)”, Bull. Acad. Polon. Sci. Ser. Math., 28:7–8 (1980), 347–350 | MR

[3] Lewicki G., Best Approximation in Spaces of Bounded Linear Operators, Diss. Math., XXXCCC, Warszawa, 1994