  Motivated by the construction of confidence intervals in statistics, we study
optimal configurations of $2^d-1$ lines in real projective space $RP^{d-1}$.
For small $d$, we determine line sets that numerically minimize a wide variety
of potential functions among all configurations of $2^d-1$ lines through the
origin. Numerical experiments verify that our findings enable to assess
efficiently the tightness of a bound arising from the statistical literature.
