MinT - Information on Result #1211254

Information on Result #1211254

Digital (178, 204, 80665)-net over F₄, using (u,Â u+v)-construction based on

digital (0, 13, 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 (165, 191, 80660)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁹¹, 80660, F₄, 26, 26) (dual of [(80660, 26), 2096969, 27]-NRT-code), using
  - OA 13-folding and stacking [i] based on linear OA(4¹⁹¹, 1048580, F₄, 26) (dual of [1048580, 1048389, 27]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁹¹, 1048586, F₄, 26) (dual of [1048586, 1048395, 27]-code), using
      - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
        linear OA(4¹⁹¹, 1048576, F₄, 26) (dual of [1048576, 1048385, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
        linear OA(4¹⁸¹, 1048576, F₄, 25) (dual of [1048576, 1048395, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        linear OA(4⁰, 10, F₄, 0) (dual of [10, 10, 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.