MinT - Information on Result #1217867

Information on Result #1217867

Digital (115, 144, 4248)-net over F₉, using (u,Â u+v)-construction based on

digital (4, 18, 30)-net over F₉, using
- net from sequence [i] based on digital (4, 29)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
    - a function field by SÃ©mirat [i]
digital (97, 126, 4218)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹²⁶, 4218, F₉, 29, 29) (dual of [(4218, 29), 122196, 30]-NRT-code), using
  - OOA 14-folding and stacking with additional row [i] based on linear OA(9¹²⁶, 59053, F₉, 29) (dual of [59053, 58927, 30]-code), using
    - discarding factors / shortening the dual code based on linear OA(9¹²⁶, 59054, F₉, 29) (dual of [59054, 58928, 30]-code), using
      - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
        linear OA(9¹²⁶, 59049, F₉, 29) (dual of [59049, 58923, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(9¹²¹, 59049, F₉, 28) (dual of [59049, 58928, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [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.