MinT - Information on Result #1210390

Information on Result #1210390

Digital (105, 120, 149807)-net over F₄, using (u,Â u+v)-construction based on

digital (2, 9, 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 (96, 111, 149797)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹¹¹, 149797, F₄, 15, 15) (dual of [(149797, 15), 2246844, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(4¹¹¹, 1048580, F₄, 15) (dual of [1048580, 1048469, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹¹¹, 1048586, F₄, 15) (dual of [1048586, 1048475, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
        linear OA(4¹¹¹, 1048576, F₄, 15) (dual of [1048576, 1048465, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(4¹⁰¹, 1048576, F₄, 14) (dual of [1048576, 1048475, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.