MinT - Information on Result #1211005

Information on Result #1211005

Digital (151, 173, 95335)-net over F₄, using (u,Â u+v)-construction based on

digital (1, 12, 9)-net over F₄, using
- net from sequence [i] based on digital (1, 8)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
digital (139, 161, 95326)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁶¹, 95326, F₄, 22, 22) (dual of [(95326, 22), 2097011, 23]-NRT-code), using
  - OA 11-folding and stacking [i] based on linear OA(4¹⁶¹, 1048586, F₄, 22) (dual of [1048586, 1048425, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
      1. linear OA(4¹⁶¹, 1048576, F₄, 22) (dual of [1048576, 1048415, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(4¹⁵¹, 1048576, F₄, 21) (dual of [1048576, 1048425, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(4⁰, 10, F₄, 0) (dual of [10, 10, 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.