What is $\pi_{31}(S^2)$, the 31st homotopy group of the 2-sphere ?

___________________________________________________________________________________________
This question has a physics motivation:

1) There are relations between (2nd and 3rd) Hopf fibrations and (2- and 3-) qubits (quantum bits) entanglement; see [Pinilla and Luthra - Hopf Fibration and Quantum Entanglement in Qubit Systems](http://arxiv.org/abs/0904.4925v1).

2) Maybe there are relations between classification of qubits entanglements and sphere homotopy groups, and  we are interested in the classification of 4-qubits entanglements.
___________________________________________________________________________________________

I tried fo find the solution on the net, with help of math [fans](https://math.stackexchange.com/questions/392293/what-is-pi-31s2/392360#392360), but without success.

[Wikipedia](http://en.wikipedia.org/wiki/Homotopy_groups_of_spheres) gives only to the 22nd group homotopy of the 2-sphere.

This article of [John Baez](http://math.ucr.edu/home/baez/week264.html) gives interesting references, like [Allen Hatcher, Stable homotopy groups of spheres](http://www.math.cornell.edu/~hatcher/stemfigs/stems.html)  or a link with braids ([Berrick, Cohen, Wong, and Wu - Configurations, braids, and homotopy groups](https://doi.org/10.1090/S0894-0347-05-00507-2)). One speaks of a book of Kochman Stanley O.: [Stable Homotopy Groups of Spheres: A Computer-Assisted Approach](https://doi.org/10.1007/BFb0083795).
___________________________________________________________________________________________

But I am totally unable to find the answer.

A subsidiary question would be: Until what rank do we know these high homotopy group of the 2-sphere?