MinT - Information on Result #1224840

Information on Result #1224840

Digital (42, 55, 174796)-net over F₃₂, using (u,Â u+v)-construction based on

digital (0, 6, 33)-net over F₃₂, using
- net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
    - the rational function field F₃₂(x) [i]
  - Niederreiter sequence [i]
digital (36, 49, 174763)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁴⁹, 174763, F₃₂, 13, 13) (dual of [(174763, 13), 2271870, 14]-NRT-code), using
  - OOA 6-folding and stacking with additional row [i] based on linear OA(32⁴⁹, 1048579, F₃₂, 13) (dual of [1048579, 1048530, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁴⁹, 1048580, F₃₂, 13) (dual of [1048580, 1048531, 14]-code), using
      - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(32⁴⁹, 1048576, F₃₂, 13) (dual of [1048576, 1048527, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(32⁴⁵, 1048576, F₃₂, 12) (dual of [1048576, 1048531, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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.