MinT - Information on Result #1209977

Information on Result #1209977

Digital (74, 84, 838872)-net over F₄, using (u,Â u+v)-construction based on

digital (1, 6, 9)-net over F₄, using
- net from sequence [i] based on digital (1, 8)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
digital (68, 78, 838863)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4⁷⁸, 838863, F₄, 10, 10) (dual of [(838863, 10), 8388552, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(4⁷⁸, 4194315, F₄, 10) (dual of [4194315, 4194237, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(8) [i] based on
      1. linear OA(4⁷⁸, 4194304, F₄, 10) (dual of [4194304, 4194226, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(4⁶⁷, 4194304, F₄, 9) (dual of [4194304, 4194237, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(4⁰, 11, F₄, 0) (dual of [11, 11, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.