MinT - Information on Result #1183732

Information on Result #1183732

Digital (130, 142, 1594325)-net over F₃, using net defined by OOA based on linear OOA(3¹⁴², 1594325, F₃, 14, 12) (dual of [(1594325, 14), 22320408, 13]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(3¹⁴², 4782976, F₃, 2, 12) (dual of [(4782976, 2), 9565810, 13]-NRT-code), using
- trace code [i] based on linear OOA(9⁷¹, 2391488, F₉, 2, 12) (dual of [(2391488, 2), 4782905, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(9⁷¹, 4782976, F₉, 12) (dual of [4782976, 4782905, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(9⁷¹, 4782969, F₉, 12) (dual of [4782969, 4782898, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(9⁶⁴, 4782969, F₉, 11) (dual of [4782969, 4782905, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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

The following results depend on this result:

	Result		Method
1	Digital (131, 143, 1594325)-net over F₃	[i]	Net Duplication
2	Digital (136, 148, 1594329)-net over F₃	[i]	(u,Â u+v)-Construction for Nets
3	Digital (137, 149, 1594332)-net over F₃	[i]
4	Digital (138, 150, 1594334)-net over F₃	[i]
5	Digital (139, 151, 1594338)-net over F₃	[i]
6	Digital (140, 152, 1594344)-net over F₃	[i]
7	Digital (141, 153, 1594350)-net over F₃	[i]
8	Digital (142, 154, 1594358)-net over F₃	[i]
9	Digital (143, 155, 1594367)-net over F₃	[i]
10	Digital (146, 158, 1594371)-net over F₃	[i]
11	Digital (147, 159, 1594378)-net over F₃	[i]
12	Digital (148, 160, 1594409)-net over F₃	[i]