TITLE: Is the 4-line of the E_2 term of the classical Adams spectral sequence known?
QUESTION [19 upvotes]: In other words:

What is $\mathrm{Ext}_{\mathcal{A}}^{4,t}(\mathbb{Z}/2,\mathbb{Z}/2)$?

If the 4-line is not known, how much is known about it?
Here, $\mathcal{A}$ is the 2-primary Steenrod algebra, $4$ is the homological degree corresponding to the Adams filtration, and $t$ is the internal grading degree.  Those $\mathrm{Ext}$ groups make up the fourth row of the classical Adams spectral sequence $E_2 = \mathrm{Ext}_{\mathcal{A}}^{s,t}(\mathbb{Z}/2,\mathbb{Z}/2)$ converging to the 2-adic completion of the $(t-s)^{\mathrm{th}}$ stable homotopy group of the sphere.
For context,  

the 1-line is generated by the classes $h_i$, $i \geq 0$, ($\mathrm{deg}\: h_i = (1,2^i)$),  
the 2-line is generated by the product classes $h_i h_j$, subject to the relations $h_i h_{i+1} = 0$ and $h_i h_j = h_j h_i$,
the 3-line is generated by two sets of classes, 

the product classes $h_i h_j h_k$, subject to the relations implied by $h_i h_{i+2}^2 = 0$, $h_{i+1}^3 = h_i^2 h_{i+2}$, $h_i h_{i+1} = 0$, and $h_i h_j = h_j h_i$,  
the Massey products $\langle h_{i+1},h_i,h_{i+2}^2 \rangle$.

REPLY [3 votes]: This old question caught my eye while looking at another question.   It is worth mentioning that s= 5 is known and the decomposables in s=6 are as well, though this is unpublished.
Tai-Wei Chen,
Determination of $Ext^{5,∗}(Z/2,Z/2)$,
Topology Appl. 158 (2011), no. 5, 660–A689,
DOI 10.1016/j.topol.2011.01.002.
Tai-Wei Chen,
The structure of decomposable elements in $Ext^{6,∗}(Z/2,Z/2)$, (2012) preprint.