MinT - Information on Result #1179418

Information on Result #1179418

Digital (77, 83, 5592415)-net over F₃, using net defined by OOA based on linear OOA(3⁸³, 5592415, F₃, 6, 6) (dual of [(5592415, 6), 33554407, 7]-NRT-code), using

appending kth column [i] based on linear OOA(3⁸³, 5592415, F₃, 5, 6) (dual of [(5592415, 5), 27961992, 7]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3³, 13, F₃, 5, 2) (dual of [(13, 5), 62, 3]-NRT-code), using
    - appending 3 arbitrary columns [i] based on linear OOA(3³, 13, F₃, 2, 2) (dual of [(13, 2), 23, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
  2. linear OOA(3²⁰, 2796201, F₃, 5, 3) (dual of [(2796201, 5), 13980985, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3²⁰, 3713024, F₃, 5, 3) (dual of [(3713024, 5), 18565100, 4]-NRT-code), using
      - appending 2 arbitrary columns [i] based on linear OOA(3²⁰, 3713024, F₃, 3, 3) (dual of [(3713024, 3), 11139052, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(3²⁰, 3713024, F₃, 2, 3) (dual of [(3713024, 2), 7426028, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3²⁰, 3713024, F₃, 3) (dual of [3713024, 3713004, 4]-code or 3713024-cap in PG(19,3)), using
        large caps in PG(u,Â 3) [i]
  3. linear OOA(3⁶⁰, 2796201, F₃, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.