After two failed attempts at constructing a line-free 154-element pattern, here is another one which finally seems to work, but requires independent checking:
This represents , where all red and blue squares are not in the set (the red ones being removed in a second run after making sure all blue ones are removing as many lines as possible). The bottom left blue square is 11111, the white one just at its right is 11112, and so on. It seems that all horizontal, vertical, and diagonal lines are indeed prohibited in the end.
Count: . Then, using Michael’s proof that , one concludes that .
I hope somebody will be able to confirm it here. If not, those interested by that method might want to discuss it here without bothering the main 700 thread.
If anything works out then we’d update the wiki, and have a look at to see if some explicit formulation for general can be inferred.
This new pattern above has a lot of permutations into it and as such makes at least more sense that the previous flawed ones.
Thanks for the replies, corrections included in green below.
New edit: a few more corrections in green, total count is at 150 now.
Edit: it seems that Terry’s line and another one can both be removed at once by doing some changes.
Unrelatedly another 3 lines were forgotten, so total at 148 now, not even as good as the lower bound by other methods.
Edit: I’m posting a follow-up here: a new programming strategy.