MinT - Information on Result #1190320

Information on Result #1190320

Digital (78, 90, 1921601)-net over F₇, using net defined by OOA based on linear OOA(7⁹⁰, 1921601, F₇, 14, 12) (dual of [(1921601, 14), 26902324, 13]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(7⁹⁰, 5764804, F₇, 2, 12) (dual of [(5764804, 2), 11529518, 13]-NRT-code), using
- trace code [i] based on linear OOA(49⁴⁵, 2882402, F₄₉, 2, 12) (dual of [(2882402, 2), 5764759, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(49⁴⁵, 5764804, F₄₉, 12) (dual of [5764804, 5764759, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(49⁴⁵, 5764805, F₄₉, 12) (dual of [5764805, 5764760, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(49⁴⁵, 5764801, F₄₉, 12) (dual of [5764801, 5764756, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(49⁴¹, 5764801, F₄₉, 11) (dual of [5764801, 5764760, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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 (79, 91, 1921601)-net over F₇	[i]	Net Duplication
2	Digital (84, 96, 1921609)-net over F₇	[i]	(u,Â u+v)-Construction for Nets
3	Digital (85, 97, 1921614)-net over F₇	[i]
4	Digital (87, 99, 1921617)-net over F₇	[i]
5	Digital (88, 100, 1921622)-net over F₇	[i]
6	Digital (89, 101, 1921651)-net over F₇	[i]
7	Digital (90, 102, 1921701)-net over F₇	[i]
8	Digital (92, 104, 1921703)-net over F₇	[i]
9	Digital (93, 105, 1921709)-net over F₇	[i]
10	Digital (94, 106, 1921751)-net over F₇	[i]
11	Digital (95, 107, 1921801)-net over F₇	[i]
12	Digital (97, 109, 1921808)-net over F₇	[i]
13	Digital (98, 110, 1921870)-net over F₇	[i]
14	Digital (97, 109, 1921809)-net over F₇	[i]