ns-lean: Naslund's Conjecture 13 is false at q = 3, k = 2, for every n congruent to 0 mod 4 with n >= 8
A Lean 4 proof that square-difference-free subsets of the polynomials of degree below n over F_3 can be larger than 3^(3n/4). Call A square-difference-free when no two of its elements differ by a nonzero square, and let D_3(n) be the largest size of such a set inside P_{3,n}. A ten-word code S in F_3^4, in which no two words differ by a vector with every coordinate in {0, 1}, drives a lift that carries a square-difference-free subset of P_{3,m} to one of P_{3,m+8} with 810 times as many elements. Iterating it from the bases {0} and B_4 = {a T^3 + b T + c (1 - T^2)} gives…
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