  We demonstrate extraction of randomness from spontaneous-emission events less
than 36 ns in the past, giving output bits with excess predictability below
$10^{-5}$ and strong metrological randomness assurances. This randomness
generation strategy satisfies the stringent requirements for unpredictable
basis choices in current "loophole-free Bell tests" of local realism [Hensen et
al., Nature (London) 526, 682 (2015); Giustina et al., Phys. Rev. Lett. 115,
250401 (2015); Shalm et al., Phys. Rev. Lett. 115, 250402 (2015)].
