MinT - Information on Result #1235331

Information on Result #1235331

Linear OOA(3²⁴⁷, 4793538, F₃, 5, 15) (dual of [(4793538, 5), 23967443, 16]-NRT-code), using extracting embedded OOA based on digital (232, 247, 4793538)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (12, 19, 54)-net over F₃, using
  - (u,Â u+v)-construction [i] based on
    1. digital (2, 5, 20)-net over F₃, using
      - net defined by OOA [i] based on linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
        doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
    2. digital (7, 14, 34)-net over F₃, using
      - linear code embedding found in a computer search [i]
2. digital (213, 228, 4793484)-net over F₃, using
  - trace code for nets [i] based on digital (42, 57, 1198371)-net over F₈₁, using
    - net defined by OOA [i] based on linear OOA(81⁵⁷, 1198371, F₈₁, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
      - OOA 7-folding and stacking with additional row [i] based on linear OA(81⁵⁷, 8388598, F₈₁, 15) (dual of [8388598, 8388541, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.