MinT - Information on Result #1211317

Information on Result #1211317

Digital (190, 217, 80674)-net over F₄, using (u,Â u+v)-construction based on

digital (3, 16, 14)-net over F₄, using
- net from sequence [i] based on digital (3, 13)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]
digital (174, 201, 80660)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4²⁰¹, 80660, F₄, 27, 27) (dual of [(80660, 27), 2177619, 28]-NRT-code), using
  - OOA 13-folding and stacking with additional row [i] based on linear OA(4²⁰¹, 1048581, F₄, 27) (dual of [1048581, 1048380, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²⁰¹, 1048586, F₄, 27) (dual of [1048586, 1048385, 28]-code), using
      - constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
        linear OA(4²⁰¹, 1048576, F₄, 27) (dual of [1048576, 1048375, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        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(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.