MinT - Information on Result #1218940

Information on Result #1218940

Digital (61, 75, 149830)-net over F₁₆, using (u,Â u+v)-construction based on

digital (2, 9, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]
digital (52, 66, 149797)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁶⁶, 149797, F₁₆, 14, 14) (dual of [(149797, 14), 2097092, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(16⁶⁶, 1048579, F₁₆, 14) (dual of [1048579, 1048513, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(16⁶⁶, 1048581, F₁₆, 14) (dual of [1048581, 1048515, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        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(16⁶¹, 1048576, F₁₆, 13) (dual of [1048576, 1048515, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.