MinT - Information on Result #1182834

Information on Result #1182834

Digital (63, 70, 2796732)-net over F₃, using net defined by OOA based on linear OOA(3⁷⁰, 2796732, F₃, 9, 7) (dual of [(2796732, 9), 25170518, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(3⁷⁰, 2796733, F₃, 3, 7) (dual of [(2796733, 3), 8390129, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁹, 532, F₃, 3, 3) (dual of [(532, 3), 1587, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁹, 532, F₃, 2, 3) (dual of [(532, 2), 1055, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁹, 532, F₃, 3) (dual of [532, 523, 4]-code or 532-cap in PG(8,3)), using
        caps completed using a computer search [i]
  2. linear OOA(3⁶¹, 2796201, F₃, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’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.