MinT - Information on Result #1214420

Information on Result #1214420

Digital (45, 54, 205895)-net over F₇, using (u,Â u+v)-construction based on

digital (0, 4, 8)-net over F₇, using
- net from sequence [i] based on digital (0, 7)-sequence over F₇, using
  - Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using
    - the rational function field F₇(x) [i]
  - Niederreiter sequence [i]
digital (41, 50, 205887)-net over F₇, using
- net defined by OOA [i] based on linear OOA(7⁵⁰, 205887, F₇, 9, 9) (dual of [(205887, 9), 1852933, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(7⁵⁰, 823549, F₇, 9) (dual of [823549, 823499, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(7⁵⁰, 823550, F₇, 9) (dual of [823550, 823500, 10]-code), using
      - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
        linear OA(7⁵⁰, 823543, F₇, 9) (dual of [823543, 823493, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(7⁴³, 823543, F₇, 8) (dual of [823543, 823500, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(7⁰, 7, F₇, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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.