Rational designs

Journal article, 2019

© 2019 The existence of designs over R on a path-connected space has been proved by Seymour and Zaslavsky. This paper studies for the first time rational designs, that is designs over Q. We establish the existence of rational designs on an open connected space under certain necessary conditions. Consequently, we show that there exist rational designs on rational simplicial complexes and spherical designs over some real abelian extension of Q.