MinT - Information on Result #1179616

Information on Result #1179616

Digital (5, 8, 1245133)-net over F₂₇, using net defined by OOA based on linear OOA(27⁸, 1245133, F₂₇, 3, 3) (dual of [(1245133, 3), 3735391, 4]-NRT-code), using

appending kth column [i] based on linear OOA(27⁸, 1245133, F₂₇, 2, 3) (dual of [(1245133, 2), 2490258, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(27⁸, 1245133, F₂₇, 3) (dual of [1245133, 1245125, 4]-code or 1245133-cap in PG(7,27)), using
  - product of projective cap with 27²-ovoid cap in AG(3,Â 27) [i] based on linear OA(27⁵, 1708, F₂₇, 3) (dual of [1708, 1703, 4]-code or 1708-cap in PG(4,27)), using
    - large caps in PG(4,Â b) [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 (28, 34, 4041334)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
2	Digital (32, 39, 4041333)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
3	Digital (79, 90, 4601245)-net over F₂₇	[i]	Generalized (u,Â u+v)-Construction for Nets
4	Digital (74, 84, 4601245)-net over F₂₇	[i]
5	Digital (78, 89, 4600769)-net over F₂₇	[i]
6	Digital (79, 90, 4601498)-net over F₂₇	[i]
7	Digital (77, 88, 4600741)-net over F₂₇	[i]
8	Digital (78, 89, 4601470)-net over F₂₇	[i]
9	Digital (73, 83, 4600741)-net over F₂₇	[i]
10	Digital (74, 84, 4601470)-net over F₂₇	[i]
11	Digital (76, 87, 4600713)-net over F₂₇	[i]
12	Digital (77, 88, 4601442)-net over F₂₇	[i]
13	Digital (79, 90, 5152566)-net over F₂₇	[i]
14	Digital (72, 82, 4600713)-net over F₂₇	[i]
15	Digital (73, 83, 4601442)-net over F₂₇	[i]
16	Digital (75, 86, 4600685)-net over F₂₇	[i]
17	Digital (76, 87, 4601414)-net over F₂₇	[i]
18	Digital (78, 89, 5152538)-net over F₂₇	[i]
19	Digital (79, 90, 5154725)-net over F₂₇	[i]
20	Digital (79, 90, 5845790)-net over F₂₇	[i]
21	Digital (71, 81, 4600685)-net over F₂₇	[i]
22	Digital (72, 82, 4601414)-net over F₂₇	[i]
23	Digital (74, 84, 5152538)-net over F₂₇	[i]
24	Digital (61, 70, 5439545)-net over F₂₇	[i]
25	Digital (74, 85, 4600657)-net over F₂₇	[i]
26	Digital (75, 86, 4601386)-net over F₂₇	[i]
27	Digital (77, 88, 5152510)-net over F₂₇	[i]
28	Digital (78, 89, 5153968)-net over F₂₇	[i]
29	Digital (78, 89, 5845762)-net over F₂₇	[i]
30	Digital (79, 90, 5847220)-net over F₂₇	[i]
31	Digital (70, 80, 4600657)-net over F₂₇	[i]
32	Digital (71, 81, 4601386)-net over F₂₇	[i]
33	Digital (73, 83, 5152510)-net over F₂₇	[i]
34	Digital (74, 84, 5153968)-net over F₂₇	[i]
35	Digital (74, 84, 5845762)-net over F₂₇	[i]
36	Digital (60, 69, 5439517)-net over F₂₇	[i]
37	Digital (61, 70, 5441704)-net over F₂₇	[i]
38	Digital (73, 84, 4600629)-net over F₂₇	[i]
39	Digital (74, 85, 4601358)-net over F₂₇	[i]
40	Digital (76, 87, 5152482)-net over F₂₇	[i]
41	Digital (77, 88, 5153211)-net over F₂₇	[i]
42	Digital (77, 88, 5845734)-net over F₂₇	[i]
43	Digital (78, 89, 5846463)-net over F₂₇	[i]
44	Digital (69, 79, 4600629)-net over F₂₇	[i]
45	Digital (70, 80, 4601358)-net over F₂₇	[i]
46	Digital (72, 82, 5152482)-net over F₂₇	[i]
47	Digital (73, 83, 5153211)-net over F₂₇	[i]
48	Digital (73, 83, 5845734)-net over F₂₇	[i]
49	Digital (74, 84, 5846463)-net over F₂₇	[i]
50	Digital (59, 68, 5439489)-net over F₂₇	[i]
51	Digital (60, 69, 5440947)-net over F₂₇	[i]
52	Digital (39, 46, 5696976)-net over F₂₇	[i]
53	Digital (94, 106, 5439433)-net over F₂₇	[i]
54	Digital (71, 82, 4600601)-net over F₂₇	[i]
55	Digital (72, 83, 4601330)-net over F₂₇	[i]
56	Digital (73, 84, 4621013)-net over F₂₇	[i]
57	Digital (74, 85, 5152454)-net over F₂₇	[i]
58	Digital (75, 86, 5845706)-net over F₂₇	[i]
59	Digital (67, 77, 4600601)-net over F₂₇	[i]
60	Digital (68, 78, 4601330)-net over F₂₇	[i]
61	Digital (69, 79, 4621013)-net over F₂₇	[i]
62	Digital (70, 80, 5152454)-net over F₂₇	[i]
63	Digital (71, 81, 5845706)-net over F₂₇	[i]
64	Digital (58, 67, 5439461)-net over F₂₇	[i]
65	Digital (59, 68, 5440190)-net over F₂₇	[i]
66	Digital (39, 46, 6531599)-net over F₂₇	[i]
67	Digital (69, 80, 4600573)-net over F₂₇	[i]
68	Digital (65, 75, 4600573)-net over F₂₇	[i]
69	Digital (56, 65, 5439433)-net over F₂₇	[i]