MinT - Information on Result #1200444

Information on Result #1200444

Digital (24, 33, 1441201)-net over F₄₉, using net defined by OOA based on linear OOA(49³³, 1441201, F₄₉, 9, 9) (dual of [(1441201, 9), 12970776, 10]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OA(49³³, 5764805, F₄₉, 9) (dual of [5764805, 5764772, 10]-code), using
- constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
  1. linear OA(49³³, 5764801, F₄₉, 9) (dual of [5764801, 5764768, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  2. linear OA(49²⁹, 5764801, F₄₉, 8) (dual of [5764801, 5764772, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
  3. 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 (57, 66, 2882402)-net over F₇	[i]	Trace Code for Nets
2	Digital (28, 37, 1441251)-net over F₄₉	[i]	(u,Â u+v)-Construction for Nets
3	Digital (29, 38, 1441252)-net over F₄₉	[i]
4	Digital (30, 39, 1442377)-net over F₄₉	[i]
5	Digital (31, 40, 1442402)-net over F₄₉	[i]
6	Digital (37, 46, 2882402)-net over F₄₉	[i]
7	Digital (46, 55, 4323653)-net over F₄₉	[i]	Generalized (u,Â u+v)-Construction for Nets
8	Digital (40, 49, 2882452)-net over F₄₉	[i]
9	Digital (41, 50, 2884804)-net over F₄₉	[i]
10	Digital (42, 51, 2888352)-net over F₄₉	[i]
11	Digital (43, 52, 3002602)-net over F₄₉	[i]
12	Digital (44, 53, 4323603)-net over F₄₉	[i]