MinT - Information on Result #1184768

Information on Result #1184768

Digital (227, 246, 1062892)-net over F₃, using net defined by OOA based on linear OOA(3²⁴⁶, 1062892, F₃, 21, 19) (dual of [(1062892, 21), 22320486, 20]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(3²⁴⁶, 3188677, F₃, 3, 19) (dual of [(3188677, 3), 9565785, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁴⁶, 3188678, F₃, 3, 19) (dual of [(3188678, 3), 9565788, 20]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3²⁰, 32, F₃, 3, 9) (dual of [(32, 3), 76, 10]-NRT-code), using
      - extracting embedded OOA [i] based on digital (11, 20, 32)-net over F₃, using
        trace code for nets [i] based on digital (1, 10, 16)-net over F₉, using
        net from sequence [i] based on digital (1, 15)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
        a function field by GarcÃa and Quoos [i]
    2. linear OOA(3²²⁶, 3188646, F₃, 3, 19) (dual of [(3188646, 3), 9565712, 20]-NRT-code), using
      - trace code [i] based on linear OOA(9¹¹³, 1594323, F₉, 3, 19) (dual of [(1594323, 3), 4782856, 20]-NRT-code), using
        OOA 3-folding [i] based on linear OA(9¹¹³, 4782969, F₉, 19) (dual of [4782969, 4782856, 20]-code), using
        an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.