  We study the space of 3d ${\cal N} = 6$ SCFTs by combining numerical
bootstrap techniques with exact results derived using supersymmetric
localization. First we derive the superconformal block decomposition of the
four-point function of the stress tensor multiplet superconformal primary. We
then use supersymmetric localization results for the ${\cal N} = 6$
$U(N)_k\times U(N+M)_{-k}$ Chern-Simons-matter theories to determine two
protected OPE coefficients for many values of $N,M,k$. These two exact inputs
are combined with the numerical bootstrap to compute precise rigorous islands
for a wide range of $N,k$ at $M=0$, so that we can non-perturbatively
interpolate between SCFTs with M-theory duals at small $k$ and string theory
duals at large $k$. We also present evidence that the localization results for
the $U(1)_{2M}\times U(1+M)_{-2M}$ theory, which has a vector-like large-$M$
limit dual to higher spin theory, saturates the bootstrap bounds for certain
protected CFT data. The extremal functional allows us to then conjecturally
reconstruct low-lying CFT data for this theory.
