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 $U(d)$ be the unitary group, let $\mathcal{S}\subset U(d)$ be a Haar random finite gate-set, and let $\nu_\mathcal{S}$ be the uniform measure supported on $\mathcal{S}$. For a…

Mahmoodian–Soltankhah–Khosrovshahi–Malik conjecture. There are no $t$-trades whose volume lies in any of these intervals; equivalently, there are no $t$-trades of volume greater th…