A(6) = 6: 775 solver answers close t = 6, and A(9) <= 13 follows by hand
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…
This excerpt details the discovery of the exact value of A(6) through extensive computation and a computer-assisted proof. It builds upon previous work establishing bounds for dimensions of anisotropic systems over certain finite fields. By combining detailed searches and logical deductions, the authors confirm that the maximum dimension A(6) for such systems is exactly 6, with implications for related problems at dimensions 9 and 10.
The work relies heavily on computational verification and logical reasoning, ultimately leading to the theorem that A(6) = 6, with no anisotropic system of dimension 7 existing for t = 6.
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