6 problems

The experiments consider deterministic and random initial point sets in the unit square, evaluated using $L_2^*$ and $L_\infty^*$ star discrepancies and optimized by projected grad…

Planar dispersion optimality conjecture. The exact value of $\liminf_{N\to\infty}N\,\mathrm{disp}(N,2)$ is $\varphi^3/\sqrt{5}$. The lower and upper bounds leave the exact value un…

Lebesgue-measure discrepancy conjecture. There exists a constant $c_d$, depending only on $d$, such that, for every finite atomic measure $\nu_N$ centered at $N$ points,

Greedy van der Corput conjecture. If the construction starts with $x_0=0$, then the van der Corput sequence is an admissible choice for the greedy selection rule.

Faure–Chaix conjecture. The preceding inequality is an equality:

An $LS$-successione "alla van der Corput" nel quadrato is a sequence of points in the square generated by the van der Corput-type $LS$ construction. A sequence of points in the squ…