MinT - Information on Result #1217532

Information on Result #1217532

Digital (61, 76, 8464)-net over F₉, using (u,Â u+v)-construction based on

digital (3, 10, 28)-net over F₉, using
- net from sequence [i] based on digital (3, 27)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [i]
digital (51, 66, 8436)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁶⁶, 8436, F₉, 15, 15) (dual of [(8436, 15), 126474, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(9⁶⁶, 59053, F₉, 15) (dual of [59053, 58987, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁶⁶, 59054, F₉, 15) (dual of [59054, 58988, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
        linear OA(9⁶⁶, 59049, F₉, 15) (dual of [59049, 58983, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(9⁶¹, 59049, F₉, 14) (dual of [59049, 58988, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.