MinT - Information on Result #1179058

Information on Result #1179058

Digital (4, 7, large)-net over F₆₄, using net defined by OOA based on linear OOA(64⁷, large, F₆₄, 3, 3), using

appending kth column [i] based on linear OOA(64⁷, large, F₆₄, 2, 3), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁷, large, F₆₄, 3) (dual of [large, large−7, 4]-code), using
  - product of projective cap with 64²-ovoid cap in AG(3,Â 64) [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
    - ovoid in PG(3,Â 64) [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 (5, 8, large)-net over F₆₄	[i]	Net Duplication
2	Digital (6, 9, large)-net over F₆₄	[i]
3	Digital (7, 10, large)-net over F₆₄	[i]
4	Digital (8, 11, large)-net over F₆₄	[i]
5	Digital (9, 12, large)-net over F₆₄	[i]
6	Digital (10, 13, large)-net over F₆₄	[i]
7	Digital (11, 14, large)-net over F₆₄	[i]
8	Digital (22, 28, 5592402)-net over F₆₄	[i]	(u,Â u+v)-Construction for Nets
9	Digital (29, 35, large)-net over F₆₄	[i]
10	Digital (32, 39, large)-net over F₆₄	[i]
11	Digital (62, 73, 5033550)-net over F₆₄	[i]	Generalized (u,Â u+v)-Construction for Nets
12	Digital (61, 72, 5033485)-net over F₆₄	[i]
13	Digital (62, 73, 5037581)-net over F₆₄	[i]
14	Digital (58, 68, 5033485)-net over F₆₄	[i]
15	Digital (60, 71, 5033420)-net over F₆₄	[i]
16	Digital (61, 72, 5037516)-net over F₆₄	[i]
17	Digital (62, 73, 5049804)-net over F₆₄	[i]
18	Digital (62, 73, 5299660)-net over F₆₄	[i]
19	Digital (57, 67, 5033420)-net over F₆₄	[i]
20	Digital (58, 68, 5037516)-net over F₆₄	[i]
21	Digital (78, 90, 5592530)-net over F₆₄	[i]
22	Digital (59, 70, 5033355)-net over F₆₄	[i]
23	Digital (60, 71, 5037451)-net over F₆₄	[i]
24	Digital (61, 72, 5045643)-net over F₆₄	[i]
25	Digital (61, 72, 5299595)-net over F₆₄	[i]
26	Digital (62, 73, 5307787)-net over F₆₄	[i]
27	Digital (62, 73, 6711010)-net over F₆₄	[i]
28	Digital (56, 66, 5033355)-net over F₆₄	[i]
29	Digital (57, 67, 5037451)-net over F₆₄	[i]
30	Digital (58, 68, 5045643)-net over F₆₄	[i]
31	Digital (58, 68, 5299595)-net over F₆₄	[i]
32	Digital (48, 57, 6291645)-net over F₆₄	[i]
33	Digital (76, 88, 5592465)-net over F₆₄	[i]
34	Digital (77, 89, 5596561)-net over F₆₄	[i]
35	Digital (78, 90, 5858705)-net over F₆₄	[i]
36	Digital (79, 91, 6990500)-net over F₆₄	[i]
37	Digital (58, 69, 5033290)-net over F₆₄	[i]
38	Digital (59, 70, 5037386)-net over F₆₄	[i]
39	Digital (60, 71, 5041482)-net over F₆₄	[i]
40	Digital (60, 71, 5299530)-net over F₆₄	[i]
41	Digital (61, 72, 5303626)-net over F₆₄	[i]
42	Digital (61, 72, 6710945)-net over F₆₄	[i]
43	Digital (62, 73, 6715041)-net over F₆₄	[i]
44	Digital (55, 65, 5033290)-net over F₆₄	[i]
45	Digital (56, 66, 5037386)-net over F₆₄	[i]
46	Digital (57, 67, 5041482)-net over F₆₄	[i]
47	Digital (57, 67, 5299530)-net over F₆₄	[i]
48	Digital (58, 68, 5303626)-net over F₆₄	[i]
49	Digital (58, 68, 6710945)-net over F₆₄	[i]
50	Digital (47, 56, 6291580)-net over F₆₄	[i]
51	Digital (48, 57, 6299772)-net over F₆₄	[i]
52	Digital (77, 90, 5592400)-net over F₆₄	[i]
53	Digital (74, 86, 5592400)-net over F₆₄	[i]
54	Digital (56, 67, 5033225)-net over F₆₄	[i]
55	Digital (57, 68, 5037321)-net over F₆₄	[i]
56	Digital (58, 69, 5299465)-net over F₆₄	[i]
57	Digital (59, 70, 6710880)-net over F₆₄	[i]
58	Digital (53, 63, 5033225)-net over F₆₄	[i]
59	Digital (54, 64, 5037321)-net over F₆₄	[i]
60	Digital (55, 65, 5299465)-net over F₆₄	[i]
61	Digital (56, 66, 6710880)-net over F₆₄	[i]
62	Digital (46, 55, 6291515)-net over F₆₄	[i]
63	Digital (47, 56, 6295611)-net over F₆₄	[i]
64	Digital (48, 57, 6557755)-net over F₆₄	[i]
65	Digital (31, 38, large)-net over F₆₄	[i]
66	Digital (54, 65, 5033160)-net over F₆₄	[i]
67	Digital (51, 61, 5033160)-net over F₆₄	[i]
68	Digital (44, 53, 6291450)-net over F₆₄	[i]
69	Digital (25, 31, 5596563)-net over F₆₄	[i]
70	Digital (26, 32, 5858707)-net over F₆₄	[i]
71	Digital (27, 33, large)-net over F₆₄	[i]