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.

Interval design

Cubature formula

Rational points

Spherical design

Hilbert-Kamke problem

Averaging set


Zhen Cui

Shanghai Jiao Tong University

Jiacheng Xia

Chalmers, Mathematical Sciences, Algebra and geometry

Ziqing Xiang

The University of Georgia

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 352 541-571

Subject Categories

Architectural Engineering


Other Humanities not elsewhere specified



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7/2/2019 2