MinT - Information on Result #1210268

Information on Result #1210268

Digital (64, 78, 2346)-net over F₄, using (u,Â u+v)-construction based on

digital (0, 7, 5)-net over F₄, using
- net from sequence [i] based on digital (0, 4)-sequence over F₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 0 and N(F) ≥ 5, using
    - the rational function field F₄(x) [i]
  - Niederreiter sequence [i]
digital (57, 71, 2341)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4⁷¹, 2341, F₄, 14, 14) (dual of [(2341, 14), 32703, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(4⁷¹, 16387, F₄, 14) (dual of [16387, 16316, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁷¹, 16391, F₄, 14) (dual of [16391, 16320, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(4⁷¹, 16384, F₄, 14) (dual of [16384, 16313, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(4⁶⁴, 16384, F₄, 13) (dual of [16384, 16320, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(4⁰, 7, F₄, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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.