Line packing in real projective space

Formal definition

• ContainerReal d-space Rᵈ, every line through the origin; an answer is n points of real projective space RPᵈ⁻¹
• SubmissionExactly n nonzero vectors, d coordinates each; a vector stands for the line it spans
• Coherenceμ² is the largest squared normalized inner product over all pairs of lines, compared directly as exact rationals by cross-multiplication$${\mu }^2=\underset{i<j}{\max }\frac{{\left(v_i·v_j\right)}^2}{{\left|v_i\right|}^2{\left|v_j\right|}^2}$$
• ScoringThe record is stored as ceil(μ²·10¹⁸); the page displays μ, rounded up at the ninth decimal
• ObjectiveMake μ², equivalently μ, as small as possible over all legal families of lines$$\underset{v_1,\dots ,v_n}{\min }{\mu }^2$$