MinT - Information on Result #1211076

Information on Result #1211076

Digital (178, 201, 381311)-net over F₄, using (u,Â u+v)-construction based on

digital (2, 13, 10)-net over F₄, using
- net from sequence [i] based on digital (2, 9)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
digital (165, 188, 381301)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁸⁸, 381301, F₄, 23, 23) (dual of [(381301, 23), 8769735, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(4¹⁸⁸, 4194312, F₄, 23) (dual of [4194312, 4194124, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁸⁸, 4194315, F₄, 23) (dual of [4194315, 4194127, 24]-code), using
      - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
        linear OA(4¹⁸⁸, 4194304, F₄, 23) (dual of [4194304, 4194116, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(4¹⁷⁷, 4194304, F₄, 22) (dual of [4194304, 4194127, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(4⁰, 11, F₄, 0) (dual of [11, 11, 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.