Additional design structures in Borwein’s parametric solution

Determine whether Borwein’s parametric solution of the one-dimensional Prouhet–Tarry–Escott problem contains design structures beyond the one identified in the paper.

Background

The paper identifies a design structure in Borwein’s degree-five parametric ideal solution of the classical one-dimensional Prouhet–Tarry–Escott problem and proves that the authors’ parametric solution is contained in Borwein’s solution over the rationals. The authors then explicitly ask whether Borwein’s broader parametric family contains additional design structures. This question remains unresolved in the paper.