MinT - Information on Result #1208205

Information on Result #1208205

Digital (75, 89, 2817)-net over F₃, using (u,Â u+v)-construction based on

digital (0, 7, 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 (68, 82, 2813)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁸², 2813, F₃, 14, 14) (dual of [(2813, 14), 39300, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(3⁸², 19691, F₃, 14) (dual of [19691, 19609, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁸², 19692, F₃, 14) (dual of [19692, 19610, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(3⁸², 19683, F₃, 14) (dual of [19683, 19601, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(3⁷³, 19683, F₃, 13) (dual of [19683, 19610, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(3⁰, 9, F₃, 0) (dual of [9, 9, 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.