A simplified solution is presented for the problem of finding a set of points and corresponding weights that will minimize the variance of the estimated value of a Chebyshev regression function at a point outside the interval of observations. This problem, among others, was solved by Kiefer and Wolfowitz  by means of game-theoretic methods. The solution here is based on a simple theorem in  and well known properties of Chebyshev systems of functions.
"A Simple Solution for Optimal Chebyshev Regression Extrapolation." Ann. Math. Statist. 37 (3) 720 - 725, June, 1966. https://doi.org/10.1214/aoms/1177699467