MinT - Information on Result #1220933

Information on Result #1220933

Digital (28, 37, 97683)-net over F₂₅, using (u,Â u+v)-construction based on

digital (0, 4, 26)-net over F₂₅, using
- net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
    - the rational function field F₂₅(x) [i]
  - Niederreiter sequence [i]
digital (24, 33, 97657)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25³³, 97657, F₂₅, 9, 9) (dual of [(97657, 9), 878880, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(25³³, 390629, F₂₅, 9) (dual of [390629, 390596, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(25³³, 390625, F₂₅, 9) (dual of [390625, 390592, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(25²⁹, 390625, F₂₅, 8) (dual of [390625, 390596, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 25⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(25⁰, 4, F₂₅, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 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.