MinT - Information on Result #1211000

Information on Result #1211000

Digital (135, 157, 23841)-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 (123, 145, 23832)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁴⁵, 23832, F₄, 22, 22) (dual of [(23832, 22), 524159, 23]-NRT-code), using
  - OA 11-folding and stacking [i] based on linear OA(4¹⁴⁵, 262152, F₄, 22) (dual of [262152, 262007, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, 262153, F₄, 22) (dual of [262153, 262008, 23]-code), using
      - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
        linear OA(4¹⁴⁵, 262144, F₄, 22) (dual of [262144, 261999, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(4¹³⁶, 262144, F₄, 21) (dual of [262144, 262008, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(4⁰, 9, F₄, 0) (dual of [9, 9, 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.