co.combinatorics - On the constants in the Cameron-Erdös conjecture on sum-free subsets.

The Cameron-Erdös conjecture was proved independently by Ben Green and Alexander Sapozhenko.

Let s(n) be the number of sum-free subsets of the set of integers {1,2,...,n}. They showed that
${ s(n) / 2^{n/2} } to C_O hbox{ or } C_E,$
for constants $C_O$ and $C_E$, as $n to infty$ through odd or even values respectively.

I would like to know what are the best known bounds for the constants $C_O$ and $C_E$?

My motivation is that I considered the conjecture in the mid-1990s and tried to determine some good lower bounds for the constants on the condition that the limits existed, of course. I have a vague recollection that Cameron and Erdös had some lower bounds in the region of 5 or 6, but I no longer have their relevant papers handy to verify this.

Looking at the sequence A007865 in the OEIS, it would seem that $C_E$ is in the region of 13.4 and that $C_O$ is in the region of 14.4. If one calculates at $s(n)/2^{n/2}$ for even n, it rises steadily from n=0 to n=36 then interestingly appears to oscillate about its limit. The sequence for odd n, from n=39 onwards, possibly does the same. It would be interesting to have some more terms.

Anyway, any information that you have on the actual values of these constants would be greatly appreciated.