Studden (1968) showed that the optimal design for estimating any specific regression coefficient or parameter is supported by one of two sets of points for Tchebycheff systems with certain symmetry properties. In this paper we consider a Tchebycheffian Spline Regression Function, defined on an interval, and show that the optimal design for estimating any specified regression coefficient is supported on the same set of points. Familiarity with the notation and terminology used in the paper of Studden referred to above is assumed.
V. N. Murty. "Optimal Designs with a Tchebycheffian Spline Regression Function." Ann. Math. Statist. 42 (2) 643 - 649, April, 1971. https://doi.org/10.1214/aoms/1177693414