MinT - Information on Result #1205382

Information on Result #1205382

Digital (57, 66, 2882402)-net over F₇, using trace code for nets based on digital (24, 33, 1441201)-net over F₄₉, using

net defined by OOA [i] 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 (58, 67, 2882402)-net over F₇	[i]	Net Duplication
2	Digital (61, 70, 2882410)-net over F₇	[i]	(u,Â u+v)-Construction for Nets
3	Digital (62, 71, 2882415)-net over F₇	[i]
4	Digital (63, 72, 2882423)-net over F₇	[i]
5	Digital (64, 73, 2882452)-net over F₇	[i]
6	Digital (65, 74, 2882502)-net over F₇	[i]
7	Digital (67, 76, 2882576)-net over F₇	[i]
8	Digital (68, 77, 2883578)-net over F₇	[i]
9	Digital (69, 78, 2884754)-net over F₇	[i]
10	Digital (71, 80, 2884805)-net over F₇	[i]
11	Digital (72, 81, 2886603)-net over F₇	[i]
12	Digital (82, 91, 5764804)-net over F₇	[i]
13	Digital (94, 103, 5771300)-net over F₇	[i]	Generalized (u,Â u+v)-Construction for Nets
14	Digital (89, 98, 5764870)-net over F₇	[i]
15	Digital (90, 99, 5764954)-net over F₇	[i]
16	Digital (92, 101, 5767319)-net over F₇	[i]
17	Digital (93, 102, 5771292)-net over F₇	[i]
18	Digital (88, 97, 5764862)-net over F₇	[i]
19	Digital (89, 98, 5764904)-net over F₇	[i]
20	Digital (89, 98, 5764944)-net over F₇	[i]
21	Digital (90, 99, 5764993)-net over F₇	[i]
22	Digital (90, 99, 5765246)-net over F₇	[i]
23	Digital (91, 100, 5767311)-net over F₇	[i]
24	Digital (92, 101, 5767360)-net over F₇	[i]
25	Digital (92, 101, 5771284)-net over F₇	[i]
26	Digital (93, 102, 5771333)-net over F₇	[i]
27	Digital (93, 102, 5786367)-net over F₇	[i]
28	Digital (94, 103, 5887312)-net over F₇	[i]
29	Digital (85, 94, 5764812)-net over F₇	[i]
30	Digital (86, 95, 5764854)-net over F₇	[i]
31	Digital (87, 96, 5764936)-net over F₇	[i]
32	Digital (88, 97, 5765238)-net over F₇	[i]
33	Digital (89, 98, 5767303)-net over F₇	[i]
34	Digital (90, 99, 5771276)-net over F₇	[i]
35	Digital (91, 100, 5786359)-net over F₇	[i]
36	Digital (92, 101, 5887304)-net over F₇	[i]
37	Digital (94, 103, 6831884)-net over F₇	[i]
38	Digital (95, 104, large)-net over F₇	[i]