MinT - Information on Result #1218789

Information on Result #1218789

Digital (49, 60, 209973)-net over F₁₆, using (u,Â u+v)-construction based on

digital (4, 9, 257)-net over F₁₆, using
- base reduction for projective spaces (embedding PG(4,256) in PG(8,16)) for nets [i] based on digital (0, 5, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]
digital (40, 51, 209716)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁵¹, 209716, F₁₆, 11, 11) (dual of [(209716, 11), 2306825, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(16⁵¹, 1048581, F₁₆, 11) (dual of [1048581, 1048530, 12]-code), using
    - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
      1. linear OA(16⁵¹, 1048576, F₁₆, 11) (dual of [1048576, 1048525, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(16⁴⁶, 1048576, F₁₆, 10) (dual of [1048576, 1048530, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.