Linear OA(7⁶⁸, 79, F₇, 45) (dual of [79, 11, 46]-code), using construction XX applied to C₁ = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}), C₂ = C([0,27]), C₃ = C₁ + C₂ = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}), and C_∩ = C₁ ∩ C₂ = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}) based on

1. linear OA(7⁴⁴, 48, F₇, 39) (dual of [48, 4, 40]-code), using the primitive cyclic code C(A) with length 48 = 7²âˆ’1, defining set A = {1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}, and minimum distance d ≥ |{−3,2,7,…,−5}|+1 = 40 (BCH-bound) [i]
2. linear OA(7⁴⁰, 48, F₇, 32) (dual of [48, 8, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 7²âˆ’1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 33 [i]
3. linear OA(7⁴⁷, 48, F₇, 47) (dual of [48, 1, 48]-code or 48-arc in PG(46,7)), using the primitive cyclic code C(A) with length 48 = 7²âˆ’1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34,41}, and minimum distance d ≥ |{3,14,25,…,−19}|+1 = 48 (BCH-bound) [i]
4. linear OA(7³⁷, 48, F₇, 26) (dual of [48, 11, 27]-code), using the primitive cyclic code C(A) with length 48 = 7²âˆ’1, defining set A = {1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}, and minimum distance d ≥ |{6,7,…,31}|+1 = 27 (BCH-bound) [i]
5. linear OA(7¹⁶, 23, F₇, 12) (dual of [23, 7, 13]-code), using
   • discarding factors / shortening the dual code based on linear OA(7¹⁶, 32, F₇, 12) (dual of [32, 16, 13]-code), using
     • extended quadratic residue code Q_e(32,7) [i]
6. linear OA(7⁵, 8, F₇, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using
   • extended Reed–Solomon code RS_e(3,7) [i]
   • the expurgated narrow-sense BCH-code C(I) with length 8 | 7²âˆ’1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]