MinT - Information on Result #1208853

Information on Result #1208853

Digital (199, 228, 12666)-net over F₃, using (u,Â u+v)-construction based on

digital (4, 18, 12)-net over F₃, using
- net from sequence [i] based on digital (4, 11)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
    - an explicitly constructive algebraic function field [i]
digital (181, 210, 12654)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3²¹⁰, 12654, F₃, 29, 29) (dual of [(12654, 29), 366756, 30]-NRT-code), using
  - OOA 14-folding and stacking with additional row [i] based on linear OA(3²¹⁰, 177157, F₃, 29) (dual of [177157, 176947, 30]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹⁰, 177158, F₃, 29) (dual of [177158, 176948, 30]-code), using
      - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
        linear OA(3²¹⁰, 177147, F₃, 29) (dual of [177147, 176937, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(3¹⁹⁹, 177147, F₃, 28) (dual of [177147, 176948, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
        linear OA(3⁰, 11, F₃, 0) (dual of [11, 11, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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.