MinT - Information on Result #1205185

Information on Result #1205185

Digital (139, 148, large)-net over F₃, using trace code for nets based on digital (28, 37, 2097231)-net over F₈₁, using

net defined by OOA [i] based on linear OOA(81³⁷, 2097231, F₈₁, 12, 9) (dual of [(2097231, 12), 25166735, 10]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(81³⁷, 2097232, F₈₁, 4, 9) (dual of [(2097232, 4), 8388891, 10]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(81⁴, 82, F₈₁, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(4;324,81) [i]
    2. linear OOA(81³³, 2097150, F₈₁, 4, 9) (dual of [(2097150, 4), 8388567, 10]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(81³³, 8388600, F₈₁, 9) (dual of [8388600, 8388567, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(81³³, large, F₈₁, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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 (140, 148, large)-net over F₃	[i]	t-Expansion
2	Digital (141, 148, large)-net over F₃	[i]
3	Digital (142, 148, large)-net over F₃	[i]
4	Digital (143, 148, large)-net over F₃	[i]
5	Digital (144, 148, large)-net over F₃	[i]
6	Digital (145, 148, large)-net over F₃	[i]
7	Digital (140, 149, large)-net over F₃	[i]	Net Duplication
8	Digital (141, 150, large)-net over F₃	[i]
9	Digital (142, 151, large)-net over F₃	[i]
10	Digital (143, 152, large)-net over F₃	[i]
11	Digital (144, 153, large)-net over F₃	[i]
12	Digital (145, 154, large)-net over F₃	[i]
13	Digital (146, 155, large)-net over F₃	[i]
14	Digital (147, 156, large)-net over F₃	[i]
15	Digital (148, 157, large)-net over F₃	[i]
16	Digital (149, 158, large)-net over F₃	[i]
17	Digital (150, 159, large)-net over F₃	[i]
18	Digital (151, 160, large)-net over F₃	[i]
19	Digital (152, 161, large)-net over F₃	[i]
20	Digital (153, 162, large)-net over F₃	[i]
21	Digital (154, 163, large)-net over F₃	[i]
22	Digital (155, 164, large)-net over F₃	[i]
23	Digital (156, 165, large)-net over F₃	[i]
24	Digital (157, 166, large)-net over F₃	[i]
25	Digital (158, 167, large)-net over F₃	[i]
26	Digital (159, 168, large)-net over F₃	[i]
27	Digital (160, 169, large)-net over F₃	[i]
28	Digital (161, 170, large)-net over F₃	[i]
29	Digital (139, 147, large)-net over F₃	[i]	m-Reduction
30	Digital (139, 146, large)-net over F₃	[i]
31	Digital (139, 145, large)-net over F₃	[i]
32	Digital (139, 144, large)-net over F₃	[i]
33	Digital (139, 143, large)-net over F₃	[i]
34	Digital (139, 142, large)-net over F₃	[i]