MinT - Information on Result #1217320

Information on Result #1217320

Digital (40, 51, 11820)-net over F₉, using (u,Â u+v)-construction based on

digital (0, 5, 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 (35, 46, 11810)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁴⁶, 11810, F₉, 11, 11) (dual of [(11810, 11), 129864, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(9⁴⁶, 59051, F₉, 11) (dual of [59051, 59005, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁴⁶, 59054, F₉, 11) (dual of [59054, 59008, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(9⁴⁶, 59049, F₉, 11) (dual of [59049, 59003, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(9⁴¹, 59049, F₉, 10) (dual of [59049, 59008, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.