MinT - Information on Result #1208002

Information on Result #1208002

Digital (188, 199, large)-net over F₃, using (u,Â u+v)-construction based on

digital (41, 46, 4194301)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁴⁶, 4194301, F₃, 5, 5) (dual of [(4194301, 5), 20971459, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴⁶, large, F₃, 5) (dual of [large, large−46, 6]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
digital (142, 153, 5033160)-net over F₃, using
- trace code for nets [i] based on digital (40, 51, 1677720)-net over F₂₇, using
  - net defined by OOA [i] based on linear OOA(27⁵¹, 1677720, F₂₇, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(27⁵¹, 8388601, F₂₇, 11) (dual of [8388601, 8388550, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁵¹, large, F₂₇, 11) (dual of [large, large−51, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (189, 199, large)-net over F₃	[i]	t-Expansion
2	Digital (190, 199, large)-net over F₃	[i]
3	Digital (191, 199, large)-net over F₃	[i]
4	Digital (192, 199, large)-net over F₃	[i]
5	Digital (193, 199, large)-net over F₃	[i]
6	Digital (194, 199, large)-net over F₃	[i]
7	Digital (195, 199, large)-net over F₃	[i]
8	Digital (196, 199, large)-net over F₃	[i]
9	Digital (189, 200, large)-net over F₃	[i]	Net Duplication
10	Digital (190, 201, large)-net over F₃	[i]
11	Digital (191, 202, large)-net over F₃	[i]
12	Digital (192, 203, large)-net over F₃	[i]
13	Digital (193, 204, large)-net over F₃	[i]
14	Digital (194, 205, large)-net over F₃	[i]
15	Digital (195, 206, large)-net over F₃	[i]
16	Digital (196, 207, large)-net over F₃	[i]
17	Digital (197, 208, large)-net over F₃	[i]
18	Digital (198, 209, large)-net over F₃	[i]
19	Digital (199, 210, large)-net over F₃	[i]
20	Digital (200, 211, large)-net over F₃	[i]
21	Digital (201, 212, large)-net over F₃	[i]
22	Digital (202, 213, large)-net over F₃	[i]
23	Digital (203, 214, large)-net over F₃	[i]
24	Digital (204, 215, large)-net over F₃	[i]
25	Digital (205, 216, large)-net over F₃	[i]
26	Digital (206, 217, large)-net over F₃	[i]
27	Digital (207, 218, large)-net over F₃	[i]
28	Digital (208, 219, large)-net over F₃	[i]
29	Digital (209, 220, large)-net over F₃	[i]
30	Digital (210, 221, large)-net over F₃	[i]
31	Digital (211, 222, large)-net over F₃	[i]
32	Digital (212, 223, large)-net over F₃	[i]
33	Digital (213, 224, large)-net over F₃	[i]
34	Digital (214, 225, large)-net over F₃	[i]
35	Digital (215, 226, large)-net over F₃	[i]
36	Digital (216, 227, large)-net over F₃	[i]
37	Digital (217, 228, large)-net over F₃	[i]
38	Digital (218, 229, large)-net over F₃	[i]
39	Digital (219, 230, large)-net over F₃	[i]
40	Digital (220, 231, large)-net over F₃	[i]
41	Digital (188, 198, large)-net over F₃	[i]	m-Reduction
42	Digital (188, 197, large)-net over F₃	[i]
43	Digital (188, 196, large)-net over F₃	[i]
44	Digital (188, 195, large)-net over F₃	[i]
45	Digital (188, 194, large)-net over F₃	[i]
46	Digital (188, 193, large)-net over F₃	[i]
47	Digital (188, 192, large)-net over F₃	[i]
48	Digital (188, 191, large)-net over F₃	[i]
49	Linear OOA(3¹⁹⁹, large, F₃, 5, 11)	[i]	Extracting Embedded OOA