MinT - Information on Result #1215320

Information on Result #1215320

Digital (79, 93, 299608)-net over F₈, using (u,Â u+v)-construction based on

digital (1, 8, 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 (71, 85, 299594)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁸⁵, 299594, F₈, 14, 14) (dual of [(299594, 14), 4194231, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(8⁸⁵, 2097158, F₈, 14) (dual of [2097158, 2097073, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁸⁵, 2097159, F₈, 14) (dual of [2097159, 2097074, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(8⁸⁵, 2097152, F₈, 14) (dual of [2097152, 2097067, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(8⁷⁸, 2097152, F₈, 13) (dual of [2097152, 2097074, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 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.