The most separated family of subspaces · n = 15
Choose n two-dimensional subspaces of R^d. The squared chordal distance of two planes is the sum of the squared sines of their principal angles — equivalently 2 − tr(P_iP_j) with P the orthogonal projectors. Maximize the smallest squared chordal distance over all pairs.
Instanced = 5, n = 15
ObjectiveMaximize the smallest squared chordal distance
Best known, unproven1.270746266Sloane's Grassmannian packing table (best packing found)
Formal definition
- ContainerReal d-space R^d; an answer is n points of the Grassmannian G(d, 2) — n planes through the origin
- SubmissionExactly n subspaces, each 2 basis vectors; the basis vectors must be linearly independent
- ObjectiveMaximize min 2 − tr(P_iP_j); projectors are built exactly through the 2×2 adjugate, rational throughout
- ScoringThe record is floor(min squared chordal distance · 10¹⁸), rounded against the submitter; the page shows the squared distance, rounded down at the ninth decimal