MinT - Information on Result #1217528

Information on Result #1217528

Digital (50, 65, 1885)-net over F₉, using (u,Â u+v)-construction based on

digital (0, 7, 10)-net over F₉, using
- net from sequence [i] based on digital (0, 9)-sequence over F₉, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 0 and N(F) ≥ 10, using
    - the rational function field F₉(x) [i]
  - Niederreiter sequence [i]
digital (43, 58, 1875)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁵⁸, 1875, F₉, 15, 15) (dual of [(1875, 15), 28067, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(9⁵⁸, 13126, F₉, 15) (dual of [13126, 13068, 16]-code), using
    - trace code [i] based on linear OA(81²⁹, 6563, F₈₁, 15) (dual of [6563, 6534, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
        linear OA(81²⁹, 6561, F₈₁, 15) (dual of [6561, 6532, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(81²⁷, 6561, F₈₁, 14) (dual of [6561, 6534, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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.