6 problems

The subunit-$L^p$ discrepancy conjecture. For every dimension $d\geq2$ and every $0<p<1$, there is a constant depending only on $d$ and $p$ such that

The $L^1$ discrepancy conjecture. For every dimension $d\geq2$, there is a constant depending only on $d$ such that

Let $d$ be the dimension, let $P$ be a point set, and let $d^{*}_{\infty}(P)$ denote its $L_{\infty}$ star discrepancy. The inverse star discrepancy problem asks for the smallest…

Let $d$ be the dimension, and consider the inverse star discrepancy problem of finding the number of points needed to obtain discrepancy at most a prescribed threshold. The inverse…

Let $P\subseteq [0,1]^d$ be a point set of size $n$, and let $d^{*}_{\infty}(P)$ denote its $L_{\infty}$ star discrepancy. The asymptotic star-discrepancy conjecture. It is conject…

Let $P\subseteq [0,1]^d$ be a point set of size $n$, and let $d^{*}_{\infty}(P)$ denote its $L_{\infty}$ star discrepancy. Niederreiter–Wozniakowski's conjecture. It is conjectured…