4 problems

Let $n\in\mathbb{N}$ and let $\mathcal{P}_{\boldsymbol{a}}$ be the class of digital nets considered in the paper, with $\boldsymbol{a}=(a_1,\ldots,a_{n-1})$. In particular, let…

Let $N$-element point set $\mathcal{P}$ in $[0,1)^2$ have star discrepancy $L_{\infty}(\mathcal{P})$ and $L_2$ discrepancy $L_2(\mathcal{P})$. Write…

Fix an integer $s$ and let $\mathcal{P}\subset[0,1)^s$ be a finite point set of cardinality $N$. Its star discrepancy is denoted by $D^*(\mathcal{P})$. Star-discrepancy order conje…

Second-order weight conjecture. It is conjectured that requiring large $\mu_2(\boldsymbol{k})$ for the elements of the dual space $\mathcal{D}$ is enough to achieve the optimal rat…