MinT - Information on Result #1766799

Information on Result #1766799

Digital (169, 186, 4194346)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁸⁶, 4194346, F₃, 2, 17) (dual of [(4194346, 2), 8388506, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁰, 45, F₃, 2, 8) (dual of [(45, 2), 70, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁰, 45, F₃, 8) (dual of [45, 25, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁰, 46, F₃, 8) (dual of [46, 26, 9]-code), using
      - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
        linear OA(3³, 11, F₃, 2) (dual of [11, 8, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
        Hamming code H(3,3) [i]
        linear OA(3⁵, 11, F₃, 4) (dual of [11, 6, 5]-code), using
        Golay code G(3) [i]
        linear OA(3¹², 24, F₃, 8) (dual of [24, 12, 9]-code), using
        extended quadratic residue code Q_e(24,3) [i]
2. linear OOA(3¹⁶⁶, 4194301, F₃, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁶⁶, 8388602, F₃, 17) (dual of [8388602, 8388436, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: 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.