To build a predictor, the output of a deterministic computer model or "code" is often treated as a realization of a stochastic process indexed by the code's input variables. The authors consider an asymptotic form of the Gaussian correlation function for the stochastic process where the correlation tends to unity. They show that the limiting best linear unbiased predictor involves Lagrange interpolating polynomials; linear model terms are implicitly included. The authors then develop optimal designs based on minimizing the limiting integrated mean squared error of prediction. They show through several examples that these designs lead to good prediction accuracy.