MinT - Information on Result #1215762

Information on Result #1215762

Digital (89, 112, 2988)-net over F₈, using (u,Â u+v)-construction based on

digital (0, 11, 9)-net over F₈, using
- net from sequence [i] based on digital (0, 8)-sequence over F₈, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
    - the rational function field F₈(x) [i]
  - Niederreiter sequence [i]
digital (78, 101, 2979)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹⁰¹, 2979, F₈, 23, 23) (dual of [(2979, 23), 68416, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(8¹⁰¹, 32770, F₈, 23) (dual of [32770, 32669, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹⁰¹, 32773, F₈, 23) (dual of [32773, 32672, 24]-code), using
      - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
        linear OA(8¹⁰¹, 32768, F₈, 23) (dual of [32768, 32667, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(8⁹⁶, 32768, F₈, 22) (dual of [32768, 32672, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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.