G-optimal exact designs for quadratic regression

Exact experimental designs are presented that minimize the maximum variance of the best linear unbiased estimator of a quadratic regression function on an interval. The main result confirms a conjecture of Constantine, Lim and Studden, which is based on earlier computations of Gaffke and Krafft (Constantine et al. [1987. Admissible and optimal exact designs for polynomial regression. J. Statist. Plann. Inference 16, 15–32], Gaffke and Krafft [1982. Exact D-optimum designs for quadratic regression. J. Roy. Statist. Soc. Ser. B 44, 394–397]).