MinT - Information on Result #1217718

Information on Result #1217718

Digital (80, 101, 5915)-net over F₉, using (u,Â u+v)-construction based on

digital (0, 10, 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 (70, 91, 5905)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁹¹, 5905, F₉, 21, 21) (dual of [(5905, 21), 123914, 22]-NRT-code), using
  - OOA 10-folding and stacking with additional row [i] based on linear OA(9⁹¹, 59051, F₉, 21) (dual of [59051, 58960, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁹¹, 59054, F₉, 21) (dual of [59054, 58963, 22]-code), using
      - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
        linear OA(9⁹¹, 59049, F₉, 21) (dual of [59049, 58958, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(9⁸⁶, 59049, F₉, 20) (dual of [59049, 58963, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
        linear OA(9⁰, 5, F₉, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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.