MinT - Information on Result #1234640

Information on Result #1234640

Digital (49, 76, 1647)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (10, 23, 387)-net over F₁₂₈, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 4, 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, 6, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈ (see above)
  3. digital (0, 13, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈ (see above)
digital (26, 53, 1260)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁵³, 1260, F₁₂₈, 27, 27) (dual of [(1260, 27), 33967, 28]-NRT-code), using
  - OOA 13-folding and stacking with additional row [i] based on linear OA(128⁵³, 16381, F₁₂₈, 27) (dual of [16381, 16328, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁵³, 16384, F₁₂₈, 27) (dual of [16384, 16331, 28]-code), using
      - an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]

Mode: Constructive and linear.

None.

None.