On the optimal arrangement of 2<i>d</i> lines in ℂ<i>d</i>

Abstract We show the optimal coherence of $2d$ lines in $\mathbb{C}^{d}$ is given by the Welch bound whenever a skew Hadamard matrix of order $d+1$ exists. Our proof uses a variant of Hadamard matrix doubling that converts any equiangular tight frame of size $\tfrac{d-1}{2} \times d$ into another one of size $d \times 2d$. Among $d \leq 160$, this produces equiangular tight frames of new sizes when $d = 11$, $35$, $39$, $43$, $47$, $59$, $67$, $71$, $83$, $95$, $103$, $107$, $111$, $119$, $123$, $127$, $131$, $143$, $151$ and $155$.