MinT - Information on Result #1210998

Information on Result #1210998

Digital (122, 144, 5973)-net over F₄, using (u,Â u+v)-construction based on

digital (4, 15, 15)-net over F₄, using
- net from sequence [i] based on digital (4, 14)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
    - an explicitly constructive algebraic function field [i]
digital (107, 129, 5958)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹²⁹, 5958, F₄, 22, 22) (dual of [(5958, 22), 130947, 23]-NRT-code), using
  - OA 11-folding and stacking [i] based on linear OA(4¹²⁹, 65538, F₄, 22) (dual of [65538, 65409, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹²⁹, 65544, F₄, 22) (dual of [65544, 65415, 23]-code), using
      - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
        linear OA(4¹²⁹, 65536, F₄, 22) (dual of [65536, 65407, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(4¹²¹, 65536, F₄, 21) (dual of [65536, 65415, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(4⁰, 8, F₄, 0) (dual of [8, 8, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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.