MinT - Information on Result #3266075

Information on Result #3266075

Digital (51, 66, 149841)-net over F₃₂, using 32¹ times duplication based on digital (50, 65, 149841)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (1, 8, 44)-net over F₃₂, using
  - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]
2. digital (42, 57, 149797)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32⁵⁷, 149797, F₃₂, 15, 15) (dual of [(149797, 15), 2246898, 16]-NRT-code), using
    - OOA 7-folding and stacking with additional row [i] based on linear OA(32⁵⁷, 1048580, F₃₂, 15) (dual of [1048580, 1048523, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
        linear OA(32⁵⁷, 1048576, F₃₂, 15) (dual of [1048576, 1048519, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(32⁵³, 1048576, F₃₂, 14) (dual of [1048576, 1048523, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.