MinT - Information on Result #1217752

Information on Result #1217752

Digital (126, 148, 434844)-net over F₉, using (u,Â u+v)-construction based on

digital (3, 14, 28)-net over F₉, using
- net from sequence [i] based on digital (3, 27)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [i]
digital (112, 134, 434816)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹³⁴, 434816, F₉, 22, 22) (dual of [(434816, 22), 9565818, 23]-NRT-code), using
  - OA 11-folding and stacking [i] based on linear OA(9¹³⁴, 4782976, F₉, 22) (dual of [4782976, 4782842, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
      1. linear OA(9¹³⁴, 4782969, F₉, 22) (dual of [4782969, 4782835, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(9¹²⁷, 4782969, F₉, 21) (dual of [4782969, 4782842, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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.