(B5) is empty: 420 solver-checked classes, and A(7) <= 8 now comes down to (B6)
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…
The research explores finite 2-groups with central involutions and their dimensions, as well as anisotropic systems over finite fields. The progression of results shows that A(6) = 6, A(7) = 9, and A(8) = 11. The focus shifts to A(7) = 8, which is now contingent on the emptiness of (B6). This paper confirms that (B5) is empty, using SAT solvers and computer-assisted methods. The solution to (B6) is currently unknown, with 68 classes remaining open.
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