  We use the numerical conformal bootstrap to study six-dimensional
$\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry
$\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal
matter saturates the unitarity bounds for arbitrary $k$. Furthermore, using the
extremal-functional method, we check that the chiral-ring relations are
correctly reproduced, extract the anomalous dimensions of low-lying long
superconformal multiplets, and find hints for novel OPE selection rules
involving type-$\mathcal{B}$ multiplets.
