Linear OA(3⁸⁷, 97, F₃, 53) (dual of [97, 10, 54]-code), using construction XX applied to C₁ = C({0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,41,53}), C₂ = C([0,44]), C₃ = C₁ + C₂ = C([0,41]), and C_∩ = C₁ ∩ C₂ = C({0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,41,44,53}) based on

1. linear OA(3⁷⁴, 80, F₃, 47) (dual of [80, 6, 48]-code), using the primitive cyclic code C(A) with length 80 = 3⁴−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,41,53}, and minimum distance d ≥ |{1,14,27,…,39}|+1 = 48 (BCH-bound) [i]
2. linear OA(3⁷⁴, 80, F₃, 50) (dual of [80, 6, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 3⁴−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 51 [i]
3. linear OA(3⁷⁸, 80, F₃, 59) (dual of [80, 2, 60]-code), using the primitive cyclic code C(A) with length 80 = 3⁴−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,41,44,53}, and minimum distance d ≥ |{3,16,29,…,37}|+1 = 60 (BCH-bound) [i]
4. linear OA(3⁷⁰, 80, F₃, 44) (dual of [80, 10, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 3⁴−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 45 [i]
5. linear OA(3³, 7, F₃, 2) (dual of [7, 4, 3]-code), using
   • discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
     • Hamming code H(3,3) [i]
6. linear OA(3⁶, 10, F₃, 5) (dual of [10, 4, 6]-code), using
   • projective code from ovoid in PG(3, 3) [i]