We obtain the first deterministic randomness extractors
for $n$-bit sources with min-entropy $\ge n^{1-\alpha}$
generated (or sampled) by single-tape Turing machines
running in time $n^{2-16 \alpha}$, for all sufficiently
small $\alpha > 0$. We also show that such machines
cannot sample a uniform $n$-bit input to the Inner
Product function together with the output.

The proofs combine a variant of the crossing-sequence
technique by Hennie [SWCT 1965] with extractors for block
sources, especially those by Chor and Goldreich [SICOMP
1988] and by Kamp, Rao, Vadhan, and Zuckerman [JCSS
2011].