MinT - Information on Result #1195462

Information on Result #1195462

Digital (71, 91, 104858)-net over F₁₆, using net defined by OOA based on linear OOA(16⁹¹, 104858, F₁₆, 20, 20) (dual of [(104858, 20), 2097069, 21]-NRT-code), using

OA 10-folding and stacking [i] based on linear OA(16⁹¹, 1048580, F₁₆, 20) (dual of [1048580, 1048489, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁹¹, 1048581, F₁₆, 20) (dual of [1048581, 1048490, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
    1. 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]
    2. linear OA(16⁸⁶, 1048576, F₁₆, 19) (dual of [1048576, 1048490, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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		Method
1	Digital (72, 92, 104858)-net over F₁₆	[i]	Net Duplication
2	Digital (81, 101, 104875)-net over F₁₆	[i]	(u,Â u+v)-Construction for Nets
3	Digital (82, 102, 104882)-net over F₁₆	[i]
4	Digital (83, 103, 104891)-net over F₁₆	[i]
5	Digital (84, 104, 104896)-net over F₁₆	[i]
6	Digital (85, 105, 104903)-net over F₁₆	[i]
7	Digital (86, 106, 104907)-net over F₁₆	[i]
8	Digital (87, 107, 104923)-net over F₁₆	[i]