MinT - Information on Result #1217191

Information on Result #1217191

Digital (39, 46, 1594335)-net over F₉, using (u,Â u+v)-construction based on

digital (0, 3, 10)-net over F₉, using
- net from sequence [i] based on digital (0, 9)-sequence over F₉, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 0 and N(F) ≥ 10, using
    - the rational function field F₉(x) [i]
  - Niederreiter sequence [i]
digital (36, 43, 1594325)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁴³, 1594325, F₉, 7, 7) (dual of [(1594325, 7), 11160232, 8]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OA(9⁴³, 4782976, F₉, 7) (dual of [4782976, 4782933, 8]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
      1. linear OA(9⁴³, 4782969, F₉, 7) (dual of [4782969, 4782926, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(9³⁶, 4782969, F₉, 6) (dual of [4782969, 4782933, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 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.