3 problems

Simplex design factorial-size conjecture. There exists a $t$-design $X\subset \mathbb{R}^d/\left(\sum_{i=1}^d x_i=-1\right)$ for $\sigma$, with $t\leq d$, such that

Let $N_*(d,t)$ be the minimal number of elements in a $t$-design in the $d$-point simplex, and let $\binom{a}{b}$ denote a binomial coefficient. Simplex-design lower-bound conjectu…

Let a cyclic $t$-design in dimension $d$ be a finite orbit of a unitary acting on quantum states whose decohered probability vectors form a simplex $t$-design. Cyclic 2-design exis…