I've got 67 just using random placements with heuristics, programmed in Python. ...

abentspoon · on Dec 1, 2009

I've placed 74 using an IP solver

      1 1 . . . . . 1 1 . . . . . 1 . .
      . 1 1 1 1 . . . . . . . . . . . .
      1 . 1 . . 1 . . . . . 1 . . . . 1
      1 . . 1 . . 1 . . . 1 . . . . 1 .
      1 . . . 1 . . . . 1 . . . 1 . . .
      . . . 1 . 1 . 1 . . . . . 1 . . .
      . 1 . . . 1 1 . . 1 . . . . . . .
      . . 1 . . . 1 1 . . . . 1 . . . .
      . . . . 1 1 . . 1 . . . 1 . . 1 .
      . . 1 . . . . . 1 1 1 . . . . . .
      . . . . 1 . . 1 . . 1 1 . . . . .
      . . . . . . 1 . 1 . . 1 . 1 . . .
      . . . 1 . . . . . 1 . 1 1 . 1 . .
      . 1 . . . . . . . . 1 . 1 1 . . 1
      . . 1 . . . . . . . . . . 1 1 1 .
      . . . . 1 . 1 . . . . . . . 1 . 1
      . . . . . . . 1 . 1 . . . . . 1 1

The solver chokes on anything larger than a 6x6 grid, but I've had good luck adding one row at a time to a smaller solution.

http://pastebin.com/m4c4696af

edit: He mentions that he already found a size 74 set in one of the linked pdfs. http://www.cs.umd.edu/~gasarch/BLOGPAPERS/17x17.pdf