MinT - Information on Result #1213472

Information on Result #1213472

Digital (40, 52, 527)-net over F₅, using (u,Â u+v)-construction based on

digital (0, 6, 6)-net over F₅, using
- net from sequence [i] based on digital (0, 5)-sequence over F₅, using
  - Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 0 and N(F) ≥ 6, using
    - the rational function field F₅(x) [i]
  - Niederreiter sequence [i]
digital (34, 46, 521)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁴⁶, 521, F₅, 12, 12) (dual of [(521, 12), 6206, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(5⁴⁶, 3126, F₅, 12) (dual of [3126, 3080, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁴⁶, 3130, F₅, 12) (dual of [3130, 3084, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(5⁴⁶, 3125, F₅, 12) (dual of [3125, 3079, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(5⁴¹, 3125, F₅, 11) (dual of [3125, 3084, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(5⁰, 5, F₅, 0) (dual of [5, 5, 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.