  We use the recently developed navigator method to obtain rigorous upper and
lower bounds on new OPE data in the 3d Ising CFT. For example, assuming that
there are only two $\mathbb{Z}_2$-even scalar operators $\epsilon$ and
$\epsilon'$ with a dimension below 6 we find a narrow allowed interval for
$\Delta_{\epsilon'}$, $\lambda_{\sigma\sigma\epsilon'}$ and
$\lambda_{\epsilon\epsilon\epsilon'}$. With similar assumptions in the
$\mathbb{Z}_2$-even spin-2 and the $\mathbb{Z}_2$-odd scalar sectors we are
also able to constrain: the central charge $c_T$; the OPE data $\Delta_{T'}$,
$\lambda_{\epsilon\epsilon T'}$ and $\lambda_{\sigma\sigma T'}$ of the second
spin-2 operator; and the OPE data $\Delta_{\sigma'}$ and
$\lambda_{\sigma\epsilon\sigma'}$ of the second $\mathbb{Z}_2$-odd scalar. We
compare the rigorous bounds we find with estimates that have been previously
obtained using the extremal functional method (EFM) and find a good match. This
both validates the EFM and shows the navigator-search method to be a feasible
and more rigorous alternative for estimating a large part of the
low-dimensional operator spectrum. We also investigate the effect of imposing
sparseness conditions on all sectors at once. We find that the island does not
greatly reduce in size under these assumptions. We efficiently find islands and
determine their size in high-dimensional parameter spaces (up to 13
parameters). This shows that using the navigator method the numerical conformal
bootstrap is no longer constrained to the exploration of small parameter
spaces.
