MinT - Information on Result #1219008

Information on Result #1219008

Digital (50, 65, 18742)-net over F₁₆, using (u,Â u+v)-construction based on

digital (0, 7, 17)-net over F₁₆, using
- net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
    - the rational function field F₁₆(x) [i]
  - Niederreiter sequence [i]
digital (43, 58, 18725)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁵⁸, 18725, F₁₆, 15, 15) (dual of [(18725, 15), 280817, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(16⁵⁸, 131076, F₁₆, 15) (dual of [131076, 131018, 16]-code), using
    - trace code [i] based on linear OA(256²⁹, 65538, F₂₅₆, 15) (dual of [65538, 65509, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
        linear OA(256²⁹, 65536, F₂₅₆, 15) (dual of [65536, 65507, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(256²⁷, 65536, F₂₅₆, 14) (dual of [65536, 65509, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 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.