Linear OA(16⁵³, 870, F₁₆, 21) (dual of [870, 817, 22]-code), using 345 step VarÅ¡amov–Edel lengthening with (r_i) = (4, 0, 1, 4 times 0, 1, 11 times 0, 1, 22 times 0, 1, 40 times 0, 1, 64 times 0, 1, 87 times 0, 1, 108 times 0) based on linear OA(16⁴², 514, F₁₆, 21) (dual of [514, 472, 22]-code), using

• trace code [i] based on linear OA(256²¹, 257, F₂₅₆, 21) (dual of [257, 236, 22]-code or 257-arc in PG(20,256)), using
  • extended Reed–Solomon code RS_e(236,256) [i]
  • the expurgated narrow-sense BCH-code C(I) with length 257 | 256²âˆ’1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  • algebraic-geometric code AG(F, Q+116P) with degQ = 3 and degP = 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
  • algebraic-geometric code AG(F, Q+77P) with degQ = 4 and degP = 3 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
  • algebraic-geometric code AG(F,47P) with degP = 5 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)