MinT - Information on Result #1208844

Information on Result #1208844

Digital (176, 205, 4222)-net over F₃, using (u,Â u+v)-construction based on

digital (0, 14, 4)-net over F₃, using
- net from sequence [i] based on digital (0, 3)-sequence over F₃, using
  - Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 0 and N(F) ≥ 4, using
    - the rational function field F₃(x) [i]
  - Niederreiter sequence [i]
digital (162, 191, 4218)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3¹⁹¹, 4218, F₃, 29, 29) (dual of [(4218, 29), 122131, 30]-NRT-code), using
  - OOA 14-folding and stacking with additional row [i] based on linear OA(3¹⁹¹, 59053, F₃, 29) (dual of [59053, 58862, 30]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁹¹, 59059, F₃, 29) (dual of [59059, 58868, 30]-code), using
      - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
        linear OA(3¹⁹¹, 59049, F₃, 29) (dual of [59049, 58858, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
        linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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.