MinT - Information on Result #1217324

Information on Result #1217324

Digital (50, 61, 106305)-net over F₉, using (u,Â u+v)-construction based on

digital (1, 6, 16)-net over F₉, using
- net from sequence [i] based on digital (1, 15)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
    - a function field by GarcÃa and Quoos [i]
digital (44, 55, 106289)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁵⁵, 106289, F₉, 11, 11) (dual of [(106289, 11), 1169124, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(9⁵⁵, 531446, F₉, 11) (dual of [531446, 531391, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁵⁵, 531447, F₉, 11) (dual of [531447, 531392, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(9⁵⁵, 531441, F₉, 11) (dual of [531441, 531386, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 9⁶âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(9⁴⁹, 531441, F₉, 10) (dual of [531441, 531392, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 9⁶âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(9⁰, 6, F₉, 0) (dual of [6, 6, 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.