How does one compute the differentials in the Adams Spectral Sequence for spheres at the prime 2 in the range $13\le t-s\le 20$? There seem to be 6 nonzero differentials, and at this point I only understand $d_2(h_4)=h^2_3h_0$.

There seem to be two methods that are used or referenced in various texts, but I haven't figured out exactly how to apply either in this context. The first is the Massey Product/Toda Product (apparently they are the same, but Massey is algebraic and works in $E_2$, and Toda is topological and works in $\pi_*^s$). The second is by building a cofiber sequences $S^0\to S^0\cup_f e^i\to S^i$ which gives a long exact sequence in both the $\pi^s_*$ and the spectral sequence itself.

If possible, could somebody point me to a resource where they use these methods in this range, or give me a hint on how I can try to do this?

Thanks a bunch -Joseph