MinT - Information on Result #1208778

Information on Result #1208778

Digital (177, 203, 13635)-net over F₃, using (u,Â u+v)-construction based on

digital (2, 15, 8)-net over F₃, using
- net from sequence [i] based on digital (2, 7)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
    - an explicitly constructive algebraic function field [i]
digital (162, 188, 13627)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3¹⁸⁸, 13627, F₃, 26, 26) (dual of [(13627, 26), 354114, 27]-NRT-code), using
  - OA 13-folding and stacking [i] based on linear OA(3¹⁸⁸, 177151, F₃, 26) (dual of [177151, 176963, 27]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁸⁸, 177158, F₃, 26) (dual of [177158, 176970, 27]-code), using
      - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
        linear OA(3¹⁸⁸, 177147, F₃, 26) (dual of [177147, 176959, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
        linear OA(3¹⁷⁷, 177147, F₃, 25) (dual of [177147, 176970, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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.