Solution (source code)

= Solution

Define
$$
Z_i=\begin{cases}1,&U_i^*\geq1/2,\\-1,&U_i^*<1/2.\end{cases}
$$
The $Z_i$ are independent <Rademacher random variables>. Sending
$$
\boxed{X_i=x_0+hZ_i}
$$
to the machine therefore produces the required independent design points.