MinT - Information on Result #1182830

Information on Result #1182830

Digital (61, 68, 2796312)-net over F₃, using net defined by OOA based on linear OOA(3⁶⁸, 2796312, F₃, 9, 7) (dual of [(2796312, 9), 25166740, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(3⁶⁸, 2796313, F₃, 3, 7) (dual of [(2796313, 3), 8388871, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁷, 112, F₃, 3, 3) (dual of [(112, 3), 329, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁷, 112, F₃, 2, 3) (dual of [(112, 2), 217, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁷, 112, F₃, 3) (dual of [112, 105, 4]-code or 112-cap in PG(6,3)), using
        doubling the cap [i] based on linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [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.