MinT - Information on Result #1182950

Information on Result #1182950

Digital (76, 84, 2097190)-net over F₃, using net defined by OOA based on linear OOA(3⁸⁴, 2097190, F₃, 12, 8) (dual of [(2097190, 12), 25166196, 9]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(3⁸⁴, 2097191, F₃, 4, 8) (dual of [(2097191, 4), 8388680, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁸, 41, F₃, 4, 4) (dual of [(41, 4), 156, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁸, 41, F₃, 3, 4) (dual of [(41, 3), 115, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 8, 41)-net over F₃, using
        nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(3⁷⁶, 2097150, F₃, 4, 8) (dual of [(2097150, 4), 8388524, 9]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3⁷⁶, 8388600, F₃, 8) (dual of [8388600, 8388524, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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.