Codebook packing in complex projective space

Formal definition

• ContainerComplex d-space Cᵈ; an answer is n points of complex projective space CPᵈ⁻¹
• SubmissionExactly n nonzero complex vectors, each d pairs [re, im]
• Coherenceμ² is the largest squared normalized Hermitian inner product over all pairs of complex projective points; numerators and denominators are rational and compared directly by cross-multiplication$${\mu }^2=\underset{i<j}{\max }\frac{{\left|⟨z_i,z_j⟩\right|}^2}{{\left|z_i\right|}^2{\left|z_j\right|}^2}$$
• 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 complex projective codebooks$$\underset{z_1,\dots ,z_n}{\min }{\mu }^2$$