Optimal configurations of lines and a statistical application
For statisticians constructing confidence intervals, this provides numerically optimal line configurations to evaluate bound tightness, though the contribution is incremental.
This work identifies optimal configurations of 2^d-1 lines in real projective space for small d, minimizing various potential functions, and demonstrates that these configurations efficiently assess the tightness of a statistical bound.
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.