MinT - Information on Result #1234651

Information on Result #1234651

Digital (37, 57, 2025)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (8, 18, 387)-net over F₁₂₈, using
- 1 times m-reduction [i] based on digital (8, 19, 387)-net over F₁₂₈, using
  - generalized (u,Â u+v)-construction [i] based on
    1. digital (0, 3, 129)-net over F₁₂₈, using
      - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
        Niederreiter sequence [i]
    2. digital (0, 5, 129)-net over F₁₂₈, using
      - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈ (see above)
    3. digital (0, 11, 129)-net over F₁₂₈, using
      - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈ (see above)
digital (19, 39, 1638)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128³⁹, 1638, F₁₂₈, 20, 20) (dual of [(1638, 20), 32721, 21]-NRT-code), using
  - OA 10-folding and stacking [i] based on linear OA(128³⁹, 16380, F₁₂₈, 20) (dual of [16380, 16341, 21]-code), using
    - discarding factors / shortening the dual code based on linear OA(128³⁹, 16384, F₁₂₈, 20) (dual of [16384, 16345, 21]-code), using
      - an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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.