MinT - Information on Result #1219018

Information on Result #1219018

Digital (67, 82, 149842)-net over F₁₆, using (u,Â u+v)-construction based on

digital (4, 11, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]
digital (56, 71, 149797)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁷¹, 149797, F₁₆, 15, 15) (dual of [(149797, 15), 2246884, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(16⁷¹, 1048580, F₁₆, 15) (dual of [1048580, 1048509, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(16⁷¹, 1048581, F₁₆, 15) (dual of [1048581, 1048510, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
        linear OA(16⁷¹, 1048576, F₁₆, 15) (dual of [1048576, 1048505, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(16⁶⁶, 1048576, F₁₆, 14) (dual of [1048576, 1048510, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(16⁰, 5, F₁₆, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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.