Linear OA(7⁵³, 64, F₇, 35) (dual of [64, 11, 36]-code), using construction XX applied to C₁ = C({1,2,3,4,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34}), C₂ = C([1,27]), C₃ = C₁ + C₂ = C({1,2,3,4,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}), and C_∩ = C₁ ∩ C₂ = C([1,34]) based on

1. linear OA(7⁴⁰, 48, F₇, 28) (dual of [48, 8, 29]-code), using the primitive cyclic code C(A) with length 48 = 7²âˆ’1, defining set A = {1,2,3,4,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34}, and minimum distance d ≥ |{7,8,…,34}|+1 = 29 (BCH-bound) [i]
2. linear OA(7³⁹, 48, F₇, 31) (dual of [48, 9, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 7²âˆ’1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 32 [i]
3. linear OA(7⁴⁴, 48, F₇, 39) (dual of [48, 4, 40]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 7²âˆ’1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 40 [i]
4. linear OA(7³⁵, 48, F₇, 25) (dual of [48, 13, 26]-code), using the primitive cyclic code C(A) with length 48 = 7²âˆ’1, defining set A = {1,2,3,4,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}, and minimum distance d ≥ |{7,8,…,31}|+1 = 26 (BCH-bound) [i]
5. linear OA(7³, 8, F₇, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,7) or 8-cap in PG(2,7)), using
   • extended Reed–Solomon code RS_e(5,7) [i]
   • oval in PG(2, 7) [i]
6. linear OA(7⁶, 8, F₇, 6) (dual of [8, 2, 7]-code or 8-arc in PG(5,7)), using
   • extended Reed–Solomon code RS_e(2,7) [i]
   • Simplex code S(2,7) [i]