MinT - Information on Result #1210991

Information on Result #1210991

Digital (104, 126, 1500)-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 (91, 113, 1490)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹¹³, 1490, F₄, 22, 22) (dual of [(1490, 22), 32667, 23]-NRT-code), using
  - OA 11-folding and stacking [i] based on linear OA(4¹¹³, 16390, F₄, 22) (dual of [16390, 16277, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹¹³, 16391, F₄, 22) (dual of [16391, 16278, 23]-code), using
      - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
        linear OA(4¹¹³, 16384, F₄, 22) (dual of [16384, 16271, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(4¹⁰⁶, 16384, F₄, 21) (dual of [16384, 16278, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(4⁰, 7, F₄, 0) (dual of [7, 7, 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.