MinT - Information on Result #1215158

Information on Result #1215158

Digital (41, 52, 6568)-net over F₈, using (u,Â u+v)-construction based on

digital (1, 6, 14)-net over F₈, using
- net from sequence [i] based on digital (1, 13)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
digital (35, 46, 6554)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁴⁶, 6554, F₈, 11, 11) (dual of [(6554, 11), 72048, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(8⁴⁶, 32771, F₈, 11) (dual of [32771, 32725, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁴⁶, 32773, F₈, 11) (dual of [32773, 32727, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(8⁴⁶, 32768, F₈, 11) (dual of [32768, 32722, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(8⁴¹, 32768, F₈, 10) (dual of [32768, 32727, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.