MinT - Information on Result #1218725

Information on Result #1218725

Digital (36, 45, 262162)-net over F₁₆, using (u,Â u+v)-construction based on

digital (0, 4, 17)-net over F₁₆, using
- net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
    - the rational function field F₁₆(x) [i]
  - Niederreiter sequence [i]
digital (32, 41, 262145)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁴¹, 262145, F₁₆, 9, 9) (dual of [(262145, 9), 2359264, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(16⁴¹, 1048581, F₁₆, 9) (dual of [1048581, 1048540, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(16⁴¹, 1048576, F₁₆, 9) (dual of [1048576, 1048535, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(16³⁶, 1048576, F₁₆, 8) (dual of [1048576, 1048540, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(16⁰, 5, F₁₆, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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.