MinT - Information on Result #1234647

Information on Result #1234647

Digital (42, 65, 1897)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (9, 20, 408)-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 (1, 12, 150)-net over F₁₂₈, using
    - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]
digital (22, 45, 1489)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁴⁵, 1489, F₁₂₈, 23, 23) (dual of [(1489, 23), 34202, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(128⁴⁵, 16380, F₁₂₈, 23) (dual of [16380, 16335, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁴⁵, 16384, F₁₂₈, 23) (dual of [16384, 16339, 24]-code), using
      - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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.