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For a real $n$-dimensional vector space of continuous functions on a compact interval, choose sites maximizing the absolute evaluation determinant in any basis. Linear independence ensures some nonzero evaluation determinant, so a maximizer exists and has distinct sites. Replacing row $i$ by evaluation at $t$ multiplies the determinant by the cardinal function ${\ell }_i(t)$. Maximality implies $|{\ell }_i(t)|\le 1$, hence the Lebesgue constant of interpolation is at most $n$. This gives a useful interpolation set without asserting that determinant maximization minimizes the Lebesgue constant of interpolation.

For distinct interpolation nodes $x_0,\dots ,x_n$, the polynomial ${\ell }_i(x)={\prod }_{j\ne i}(x-x_j)/(x_i-x_j)$ has ${\ell }_i(x_j)={\delta }_{ij}$. These cardinal polynomials form a basis of the polynomials of degree at most $n$, and give $p(x)={\sum }_{i}p(x_i){\ell }_i(x)$.