MinT - Information on Result #1210277

Information on Result #1210277

Digital (95, 109, 149807)-net over F₄, using (u,Â u+v)-construction based on

digital (1, 8, 9)-net over F₄, using
- net from sequence [i] based on digital (1, 8)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
digital (87, 101, 149798)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁰¹, 149798, F₄, 14, 14) (dual of [(149798, 14), 2097071, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(4¹⁰¹, 1048586, F₄, 14) (dual of [1048586, 1048485, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. 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]
      2. linear OA(4⁹¹, 1048576, F₄, 13) (dual of [1048576, 1048485, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. 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.