MinT - Information on Result #1187486

Information on Result #1187486

Digital (165, 191, 80660)-net over F₄, using net defined by OOA based on linear OOA(4¹⁹¹, 80660, F₄, 26, 26) (dual of [(80660, 26), 2096969, 27]-NRT-code), using

OA 13-folding and stacking [i] based on linear OA(4¹⁹¹, 1048580, F₄, 26) (dual of [1048580, 1048389, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁹¹, 1048586, F₄, 26) (dual of [1048586, 1048395, 27]-code), using
  - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
    1. linear OA(4¹⁹¹, 1048576, F₄, 26) (dual of [1048576, 1048385, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    2. linear OA(4¹⁸¹, 1048576, F₄, 25) (dual of [1048576, 1048395, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    3. linear OA(4⁰, 10, F₄, 0) (dual of [10, 10, 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

The following results depend on this result:

	Result		Method
1	Digital (166, 192, 80660)-net over F₄	[i]	Net Duplication
2	Digital (167, 193, 80660)-net over F₄	[i]	Net Duplication
3	Digital (178, 204, 80665)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
4	Digital (179, 205, 80669)-net over F₄	[i]
5	Digital (180, 206, 80670)-net over F₄	[i]
6	Digital (181, 207, 80674)-net over F₄	[i]
7	Digital (182, 208, 80675)-net over F₄	[i]
8	Digital (183, 209, 80677)-net over F₄	[i]