MinT - Information on Result #1211470

Information on Result #1211470

Digital (228, 258, 279626)-net over F₄, using (u,Â u+v)-construction based on

digital (0, 15, 5)-net over F₄, using
- net from sequence [i] based on digital (0, 4)-sequence over F₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 0 and N(F) ≥ 5, using
    - the rational function field F₄(x) [i]
  - Niederreiter sequence [i]
digital (213, 243, 279621)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4²⁴³, 279621, F₄, 30, 30) (dual of [(279621, 30), 8388387, 31]-NRT-code), using
  - OA 15-folding and stacking [i] based on linear OA(4²⁴³, 4194315, F₄, 30) (dual of [4194315, 4194072, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
      1. linear OA(4²⁴³, 4194304, F₄, 30) (dual of [4194304, 4194061, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(4²³², 4194304, F₄, 29) (dual of [4194304, 4194072, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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.