MinT - Information on Result #1234539

Information on Result #1234539

Digital (56, 76, 53390)-net over F₈₁, using (u,Â u+v)-construction based on

digital (8, 18, 246)-net over F₈₁, using
- 1 times m-reduction [i] based on digital (8, 19, 246)-net over F₈₁, using
  - generalized (u,Â u+v)-construction [i] based on
    1. digital (0, 3, 82)-net over F₈₁, using
      - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
    2. digital (0, 5, 82)-net over F₈₁, using
      - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)
    3. digital (0, 11, 82)-net over F₈₁, using
      - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)
digital (38, 58, 53144)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁵⁸, 53144, F₈₁, 20, 20) (dual of [(53144, 20), 1062822, 21]-NRT-code), using
  - OA 10-folding and stacking [i] based on linear OA(81⁵⁸, 531440, F₈₁, 20) (dual of [531440, 531382, 21]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁵⁸, 531441, F₈₁, 20) (dual of [531441, 531383, 21]-code), using
      - an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’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.