MinT - Information on Result #1214509

Information on Result #1214509

Digital (58, 69, 164717)-net over F₇, using (u,Â u+v)-construction based on

digital (0, 5, 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 (53, 64, 164709)-net over F₇, using
- net defined by OOA [i] based on linear OOA(7⁶⁴, 164709, F₇, 11, 11) (dual of [(164709, 11), 1811735, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(7⁶⁴, 823546, F₇, 11) (dual of [823546, 823482, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(7⁶⁴, 823550, F₇, 11) (dual of [823550, 823486, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(7⁶⁴, 823543, F₇, 11) (dual of [823543, 823479, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(7⁵⁷, 823543, F₇, 10) (dual of [823543, 823486, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.