  We show the optimal coherence of $2d$ lines in $\mathbb{C}^{d}$ is given by
the Welch bound whenever a skew Hadamard of order $d+1$ exists. Our proof uses
a variant of Hadamard doubling that converts any equiangular tight frame of
size $\tfrac{d-1}{2} \times d$ into another one of size $d \times 2d$. Among $d
< 150$, this produces equiangular tight frames of new sizes when $d = 11$,
$35$, $39$, $43$, $47$, $59$, $67$, $71$, $83$, $95$, $103$, $107$, $111$,
$119$, $123$, $127$, $131$, and $143$.
