MinT - Information on Result #1217376

Information on Result #1217376

Digital (65, 77, 797172)-net over F₉, using (u,Â u+v)-construction based on

digital (0, 6, 10)-net over F₉, using
- net from sequence [i] based on digital (0, 9)-sequence over F₉, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 0 and N(F) ≥ 10, using
    - the rational function field F₉(x) [i]
  - Niederreiter sequence [i]
digital (59, 71, 797162)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁷¹, 797162, F₉, 12, 12) (dual of [(797162, 12), 9565873, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(9⁷¹, 4782972, F₉, 12) (dual of [4782972, 4782901, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁷¹, 4782976, F₉, 12) (dual of [4782976, 4782905, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(9⁶⁴, 4782969, F₉, 11) (dual of [4782969, 4782905, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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.