Diff between goptuna Sobol sequence and scipy.stats.qmc.Sobol

[chinsoon12]

Hi,

Thank you so much on your work for Go optuna.

There are differences between the Sobol sequence generated using goptuna Sobol Engine Draw versus scipy.stats.qmc.Sobol.
Tracing the problem points to the wrong set of direction numbers being used.

In func initDirectionNumbers from https://github.com/c-bata/goptuna/blob/main/sobol/engine.go, instead of

dn := directionNumbers[j]

it should be

dn := directionNumbers[j-1]