MinT - Information on Result #1211323

Information on Result #1211323

Digital (209, 236, 322649)-net over F₄, using (u,Â u+v)-construction based on

digital (2, 15, 10)-net over F₄, using
- net from sequence [i] based on digital (2, 9)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
digital (194, 221, 322639)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4²²¹, 322639, F₄, 27, 27) (dual of [(322639, 27), 8711032, 28]-NRT-code), using
  - OOA 13-folding and stacking with additional row [i] based on linear OA(4²²¹, 4194308, F₄, 27) (dual of [4194308, 4194087, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²²¹, 4194315, F₄, 27) (dual of [4194315, 4194094, 28]-code), using
      - constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
        linear OA(4²²¹, 4194304, F₄, 27) (dual of [4194304, 4194083, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(4²¹⁰, 4194304, F₄, 26) (dual of [4194304, 4194094, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
        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.