Geodesic
Minimal projections and largest simplices
Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 1, pp. 3-10.

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It is proved that the minimal norm $\theta_n$ of a projection in linear interpolation on the $n$-dimensional cube $Q_n=[0,1]^n$ satisfies the condition $\theta_n=O(n^{1/2})$, $n\in\mathrm{N}$. With the previous results of the author it means that $\theta_n\approx n^{1/2}$. The upper estimates are provided by the projection with knots of interpolation in vertices of а largest simplex in $Q_n$. 
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M. V. Nevskij. Minimal projections and largest simplices. Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/MAIS_2007_14_1_a0/

[1] M. V. Nevskii, I. P. Irodova, Nekotopye vopposy teopii ppiblizheniya funktsii, uchebnoe posobie, YapGU, Yaposlavl, 1999, 92 pp.

[2] M. V. Nevskii, “Otsenki dlya minimalnoi nopmy ppoektopa ppi lineinoi inteppolyatsii po vepshinam $n$-mepnogo kuba”, Modelipovanie i analiz infopmatsionnykh sistem, 10:1 (2003), 9–19

[3] M. V. Nevskii, “Geometricheskie metody v zadache o minimalnom proektore”, Modelipovanie i analiz infopmatsionnykh sistem, 13:2 (2006), 16–29

[4] M. V. Nevskii, Geometricheskie konstruktsii v zadache ob optimalnoi lineinoi interpolyatsii na $n$-mernom kube, Dep. v VINITI 13.06.2006, No 785-B2006, Yarosl. gos. un-t, Yaposlavl, 2006, 21 pp.

[5] M. Hudelson, V. Klee, D. Larman, “Largest $j$-simplices in $d$-cubes: some relatives of the Hadamard maximum determinant problem”, Linear Algebra Appl., 241-243 (1996), 519–598 | DOI | MR | Zbl

[6] M. Lassak, “Parallelotopes of maximum volume in a simplex”, Discrete Comput. Geom., 21 (1999), 449–462 | DOI | MR | Zbl