Arrange 22 to 25 points to make a maximal number of lines of 4 points, with no more than 4 points on any line. Current records at Tree Planting Problems and A006065. By removing the first 0, 1, 2, or 3 points, we establish that 25, 24, 23, 22 points can make at least 32, 30, 28, 26 lines of 4. These records seem soft.
The 25 points: {{1/65,-9/65}, {1,-1}, {-19/45,-29/45}, {-1,-1}, {-1/75,34/75}, {7/25,12/25}, {19/45,29/45}, {-13/15,-8/15}, {-1/5,2/15}, {-1/25,9/25}, {19/75,29/75}, {13/45,8/45}, {1/3,1/3}, {7/15,-13/15}, {3/5,-2/5}, {-3/5,2/5}, {-7/15,13/15}, {-7/45,13/45}, {-1/15,3/5}, {1/10,7/20}, {13/15,8/15}, {0,0}, {1/15,7/30}, {1/5,7/10}, {1,1}}
I believe these records are soft because the first three points can be replaced in many ways.
What are the optimal number of lines of 4 for 22 to 25 points?