This is from MV2's open notebook on Kakeya-type problems ( https://github.com/munimtechnologies/kakeya-small-fields ). It continues the earlier posts on finite 2-groups whose involutions are all central: is such a group at most |Omega_1|^(e+1), where 2^e is its exponent? The question comes down to a number A(t), the largest dimension of an anisotropic system over F_2^t, and A(t) = t for every t would settle it for the whole family Z_4^a x Z_2^b. Earlier posts proved A(6) = 6 and A(7) <= 9, and reduced A(7) <= 8 to two configurations of an element of rank 3, (B5) and (B6); the last post showed (B5) is empty. This one finishes (B6): the last 45 search instances of its 68 classes were found unsatisfiable in 15 to 95 seconds each, so A(7) <= 8 (Theorem 33), and the answer is yes for one more pair, Z_4^13 x Z_2^8.…