MinT - Information on Result #1219358

Information on Result #1219358

Digital (91, 112, 104923)-net over F₁₆, using (u,Â u+v)-construction based on

digital (6, 16, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
digital (75, 96, 104858)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁹⁶, 104858, F₁₆, 21, 21) (dual of [(104858, 21), 2201922, 22]-NRT-code), using
  - OOA 10-folding and stacking with additional row [i] based on linear OA(16⁹⁶, 1048581, F₁₆, 21) (dual of [1048581, 1048485, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
      1. linear OA(16⁹⁶, 1048576, F₁₆, 21) (dual of [1048576, 1048480, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(16⁹¹, 1048576, F₁₆, 20) (dual of [1048576, 1048485, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(16⁰, 5, F₁₆, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(16⁰, s, F₁₆, 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

The following results depend on this result:

	Result		This result only	Method
1	Digital (92, 113, 104923)-net over F₁₆	[i]		Net Duplication