MinT - Information on Result #1193168

Information on Result #1193168

Digital (51, 58, 5609621)-net over F₉, using net defined by OOA based on linear OOA(9⁵⁸, 5609621, F₉, 9, 7) (dual of [(5609621, 9), 50486531, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(9⁵⁸, 5609622, F₉, 3, 7) (dual of [(5609622, 3), 16828808, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9⁸, 17220, F₉, 3, 3) (dual of [(17220, 3), 51652, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(9⁸, 17220, F₉, 2, 3) (dual of [(17220, 2), 34432, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁸, 17220, F₉, 3) (dual of [17220, 17212, 4]-code or 17220-cap in PG(7,9)), using
        product of projective cap with cap in AG(4,Â 9) [i] based on linear OA(9⁴, 82, F₉, 3) (dual of [82, 78, 4]-code or 82-cap in PG(3,9)), using
        ovoid in PG(3,Â 9) [i]
  2. linear OOA(9⁵⁰, 5592402, F₉, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
    - trace code [i] based on linear OOA(81²⁵, 2796201, F₈₁, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(81²⁵, large, F₈₁, 7) (dual of [large, large−25, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.