MinT - Information on Result #1208204

Information on Result #1208204

Digital (66, 80, 942)-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 (59, 73, 938)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁷³, 938, F₃, 14, 14) (dual of [(938, 14), 13059, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(3⁷³, 6566, F₃, 14) (dual of [6566, 6493, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁷³, 6569, F₃, 14) (dual of [6569, 6496, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(3⁷³, 6561, F₃, 14) (dual of [6561, 6488, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(3⁶⁵, 6561, F₃, 13) (dual of [6561, 6496, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(3⁰, 8, F₃, 0) (dual of [8, 8, 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.