3 problems

Let $e$ be a positive integer, let $\varepsilon_S$ denote the parameter used in the source, and let $[x]$ denote the integer-part notation in the source. Consider a tight Euclidean…

Let $e$ be a positive integer, and let a tight Euclidean $2e$-design be a tight Euclidean design of strength $2e$ in $\mathbb{R}^n$. A regular simplex is the standard simplex confi…

A Euclidean $t$-design is a finite weighted set $({\cal X},w)$ in $\mathbb{R}^n$ satisfying the Euclidean design integration identity for every polynomial of total degree at most…