MinT - Information on Result #1194652

Information on Result #1194652

Digital (97, 126, 4218)-net over F₉, using net defined by OOA based on linear OOA(9¹²⁶, 4218, F₉, 29, 29) (dual of [(4218, 29), 122196, 30]-NRT-code), using

OOA 14-folding and stacking with additional row [i] based on linear OA(9¹²⁶, 59053, F₉, 29) (dual of [59053, 58927, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(9¹²⁶, 59054, F₉, 29) (dual of [59054, 58928, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
    1. linear OA(9¹²⁶, 59049, F₉, 29) (dual of [59049, 58923, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(9¹²¹, 59049, F₉, 28) (dual of [59049, 58928, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
    3. linear OA(9⁰, 5, F₉, 0) (dual of [5, 5, 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 (98, 127, 4218)-net over F₉	[i]	Net Duplication
2	Digital (99, 128, 4218)-net over F₉	[i]
3	Digital (100, 129, 4218)-net over F₉	[i]
4	Digital (111, 140, 4228)-net over F₉	[i]	(u,Â u+v)-Construction for Nets
5	Digital (112, 141, 4234)-net over F₉	[i]
6	Digital (113, 142, 4238)-net over F₉	[i]
7	Digital (114, 143, 4246)-net over F₉	[i]
8	Digital (115, 144, 4248)-net over F₉	[i]
9	Digital (116, 145, 4250)-net over F₉	[i]
10	Digital (117, 146, 4252)-net over F₉	[i]
11	Digital (118, 147, 4254)-net over F₉	[i]
12	Digital (119, 148, 4258)-net over F₉	[i]
13	(121, 150, 4266)-net in base 9	[i]