Error-correcting codes vs. low-dispersion point sets
Sprache des Vortragstitels:
ICIAM2019 "International congress on Industrial and Applied Mathematics, July 15 - 19, 2019, Valencia"
Sprache des Tagungstitel:
In the last years there was an increasing interest in point sets with ?small? dispersion, i.e., in point sets that intersect each axis-parallel box with ?large? volume, especially in high dimensions. Despite the many existence results, there was only some progress regarding the actual construction. Here, we show how to generate sets, whose size is optimal with respect to the dimension d, using certain error-correcting codes. The running-time of the procedure depends polynomially on d.