TITLE: Unstable homotopy groups of spheres beyond Toda's range
QUESTION [30 upvotes]: In 1962 Toda published his book "Composition methods in homotopy groups of spheres", which contains computations of $\pi_{n+k}(S^n)$ for $k\le 19$ and $n\le 20$. The values of these groups are conveniently tabulated, and reproduced on the Wikipedia page Homotopy groups of spheres. The computations involve composition product, Toda brackets and the EHP sequence, as well as cohomology operations for the higher values of $k$.
I am fairly certain that more values of $\pi_{n+k}(S^n)$ have been computed in the intervening years, perhaps with more modern methods such as the unstable Adams spectral sequence.

Does anybody know of an up-to-date table of known unstable homotopy groups of spheres, beyond the range shown in Toda's tables?

REPLY [19 votes]: By following Ryan's leads I've been able to find references computing $\pi_{n+k}(S^n)$ for $20\leq k \leq 30$ at the prime $2$ (and in some cases at odd primes as well). I thought I'd post these as an answer for ease of reference.

M. Mimura, H. Toda, The (n+20)-th homotopy groups of n-spheres, J. Math. Kyoto Univ. 3 1963 37–58. [Contains $\pi_{n+20}(S^n)$ for all $n$ and at all primes]
M. Mimura, On the generalized Hopf homomorphism and the higher composition,
Parts I, II. J. Math. Kyoto Univ., 4, 171-190, 301-326 (1964/5). [Contains $\pi_{n+21}(S^n)$ and $\pi_{n+22}(S^n)$ for all $n$ and at all primes. For odd primes the author refers to work of Toda later published as a series of papers On iterated suspensions I--IV, J. Math. Kyoto Univ (1966/68).]
M. Mimura, M. Mori, N. Oda, Determination of 2-components of the 23- and 24-stems in homotopy groups of spheres, Mem. Fac. Sci. Kyushu Univ. Ser. A 29 (1975), no. 1, 1–42. [Contains $\pi_{n+23}(S^n)$ and $\pi_{n+24}(S^n)$ for all $n$ at the prime $2$]
N. Oda, On the 2-components of the unstable homotopy groups of spheres Parts I, II, Proc. Japan Acad. 53, Ser. A(1977), no. 6/7, 202-205/215-218. [Contains $\pi_{n+k}(S^n)$ for $25\leq k\leq 30$ for all $n$ at the prime $2$, and partial results for $31\leq k\leq 33$]

The methods are as in Toda's book. I would be interested to learn of any later references, or errata to the above.