MinT - Information on Result #1211253

Information on Result #1211253

Digital (164, 190, 20182)-net over F₄, using (u,Â u+v)-construction based on

digital (5, 18, 17)-net over F₄, using
- net from sequence [i] based on digital (5, 16)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]
digital (146, 172, 20165)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁷², 20165, F₄, 26, 26) (dual of [(20165, 26), 524118, 27]-NRT-code), using
  - OA 13-folding and stacking [i] based on linear OA(4¹⁷², 262145, F₄, 26) (dual of [262145, 261973, 27]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁷², 262153, F₄, 26) (dual of [262153, 261981, 27]-code), using
      - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
        linear OA(4¹⁷², 262144, F₄, 26) (dual of [262144, 261972, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
        linear OA(4¹⁶³, 262144, F₄, 25) (dual of [262144, 261981, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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.