MinT - Information on Result #1213598

Information on Result #1213598

Digital (73, 87, 11173)-net over F₅, using (u,Â u+v)-construction based on

digital (2, 9, 12)-net over F₅, using
- net from sequence [i] based on digital (2, 11)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 2 and N(F) ≥ 12, using
    - an explicitly constructive algebraic function field [i]
digital (64, 78, 11161)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁷⁸, 11161, F₅, 14, 14) (dual of [(11161, 14), 156176, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(5⁷⁸, 78127, F₅, 14) (dual of [78127, 78049, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁷⁸, 78132, F₅, 14) (dual of [78132, 78054, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(5⁷⁸, 78125, F₅, 14) (dual of [78125, 78047, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(5⁷¹, 78125, F₅, 13) (dual of [78125, 78054, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(5⁰, 7, F₅, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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.