It is impossible for 3SAT to have sub-exponential algorithms unless the exponential time hypothesis (ETH)exponential time hypothesis is false.
For the Upper bound, 3-SAT has randomized algorithm with expected running time $O({1.324}^n)$
- Kazuo Iwama, Suguru Tamaki, Improved upper bounds for 3-SAT, 2004.
Improved upper bounds for 3-SAT, Kazuo Iwama, Suguru Tamaki, foo
randomized algorithm with expected running time $O({1.324}^n)$ for 3SAT.
Actually, Daniel Rolf improved Kazuo Iwama, Suguru Tamaki result to $O({1.32216}^n)$
- Daniel Rolf, Improved Bound for the PPSZ/Schoning-Algorithm for 3-SAT, 2005.
Improved Bound for the PPSZ/Schoning-Algorithm for 3-SAT, Daniel Rolf,
randomized algorithm with expected running time $O({1.32216}^n)$ for 3SAT.