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].