MinT - Information on Result #1179618

Information on Result #1179618

Digital (6, 9, large)-net over F₂₇, using net defined by OOA based on linear OOA(27⁹, large, F₂₇, 3, 3), using

appending kth column [i] based on linear OOA(27⁹, large, F₂₇, 2, 3), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(27⁹, large, F₂₇, 3) (dual of [large, large−9, 4]-code), using
  - product of projective cap with (hyper)oval [i] based on linear OA(27⁷, 532899, F₂₇, 3) (dual of [532899, 532892, 4]-code or 532899-cap in PG(6,27)), using
    - product of two caps with tangent hyperplane [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 (7, 10, large)-net over F₂₇	[i]	Net Duplication
2	Digital (8, 11, large)-net over F₂₇	[i]
3	Digital (9, 12, large)-net over F₂₇	[i]
4	Digital (10, 13, large)-net over F₂₇	[i]
5	Digital (11, 14, large)-net over F₂₇	[i]
6	Digital (12, 15, large)-net over F₂₇	[i]
7	Digital (13, 16, large)-net over F₂₇	[i]
8	Digital (14, 17, large)-net over F₂₇	[i]
9	Digital (15, 18, large)-net over F₂₇	[i]
10	Digital (16, 19, large)-net over F₂₇	[i]
11	Digital (17, 20, large)-net over F₂₇	[i]
12	Digital (18, 21, large)-net over F₂₇	[i]
13	Digital (29, 35, 5592402)-net over F₂₇	[i]	(u,Â u+v)-Construction for Nets
14	Digital (32, 38, 5592458)-net over F₂₇	[i]
15	Digital (33, 39, 5593862)-net over F₂₇	[i]
16	Digital (34, 40, 5595818)-net over F₂₇	[i]
17	Digital (35, 41, 5633394)-net over F₂₇	[i]
18	Digital (36, 42, 6658200)-net over F₂₇	[i]
19	Digital (37, 43, 8082668)-net over F₂₇	[i]
20	Digital (38, 44, large)-net over F₂₇	[i]
21	Digital (33, 40, 5592400)-net over F₂₇	[i]
22	Digital (36, 43, 5592456)-net over F₂₇	[i]
23	Digital (37, 44, 5593860)-net over F₂₇	[i]
24	Digital (38, 45, 5595816)-net over F₂₇	[i]
25	Digital (39, 46, 5633392)-net over F₂₇	[i]
26	Digital (40, 47, 6658198)-net over F₂₇	[i]
27	Digital (41, 48, 8082666)-net over F₂₇	[i]
28	Digital (42, 49, large)-net over F₂₇	[i]
29	Digital (79, 90, 5033356)-net over F₂₇	[i]	Generalized (u,Â u+v)-Construction for Nets
30	Digital (78, 89, 5033328)-net over F₂₇	[i]
31	Digital (79, 90, 5034057)-net over F₂₇	[i]
32	Digital (74, 84, 5033328)-net over F₂₇	[i]
33	Digital (77, 88, 5033300)-net over F₂₇	[i]
34	Digital (78, 89, 5034029)-net over F₂₇	[i]
35	Digital (73, 83, 5033300)-net over F₂₇	[i]
36	Digital (74, 84, 5034029)-net over F₂₇	[i]
37	Digital (76, 87, 5033272)-net over F₂₇	[i]
38	Digital (77, 88, 5034001)-net over F₂₇	[i]
39	Digital (72, 82, 5033272)-net over F₂₇	[i]
40	Digital (73, 83, 5034001)-net over F₂₇	[i]
41	Digital (75, 86, 5033244)-net over F₂₇	[i]
42	Digital (76, 87, 5033973)-net over F₂₇	[i]
43	Digital (79, 90, 6710936)-net over F₂₇	[i]
44	Digital (71, 81, 5033244)-net over F₂₇	[i]
45	Digital (72, 82, 5033973)-net over F₂₇	[i]
46	Digital (61, 70, 6291534)-net over F₂₇	[i]
47	Digital (97, 109, 5592428)-net over F₂₇	[i]
48	Digital (98, 110, 5593157)-net over F₂₇	[i]
49	Digital (74, 85, 5033216)-net over F₂₇	[i]
50	Digital (75, 86, 5033945)-net over F₂₇	[i]
51	Digital (78, 89, 6710908)-net over F₂₇	[i]
52	Digital (79, 90, 6711637)-net over F₂₇	[i]
53	Digital (70, 80, 5033216)-net over F₂₇	[i]
54	Digital (71, 81, 5033945)-net over F₂₇	[i]
55	Digital (74, 84, 6710908)-net over F₂₇	[i]
56	Digital (60, 69, 6291506)-net over F₂₇	[i]
57	Digital (61, 70, 6292964)-net over F₂₇	[i]
58	Digital (95, 107, 5592400)-net over F₂₇	[i]
59	Digital (72, 83, 5033188)-net over F₂₇	[i]
60	Digital (73, 84, 5033917)-net over F₂₇	[i]
61	Digital (76, 87, 6710880)-net over F₂₇	[i]
62	Digital (68, 78, 5033188)-net over F₂₇	[i]
63	Digital (69, 79, 5033917)-net over F₂₇	[i]
64	Digital (72, 82, 6710880)-net over F₂₇	[i]
65	Digital (59, 68, 6291478)-net over F₂₇	[i]
66	Digital (60, 69, 6292207)-net over F₂₇	[i]
67	Digital (61, 70, 6311890)-net over F₂₇	[i]
68	Digital (37, 44, 5593914)-net over F₂₇	[i]
69	Digital (38, 45, 5633280)-net over F₂₇	[i]
70	Digital (39, 46, 6696162)-net over F₂₇	[i]
71	Digital (33, 39, 5593916)-net over F₂₇	[i]
72	Digital (34, 40, 5633282)-net over F₂₇	[i]
73	Digital (70, 81, 5033160)-net over F₂₇	[i]
74	Digital (66, 76, 5033160)-net over F₂₇	[i]
75	Digital (57, 66, 6291450)-net over F₂₇	[i]
76	Digital (35, 42, 5592428)-net over F₂₇	[i]
77	Digital (36, 43, 5593157)-net over F₂₇	[i]
78	Digital (37, 44, 5612840)-net over F₂₇	[i]
79	Digital (38, 45, 6144281)-net over F₂₇	[i]
80	Digital (39, 46, 8388600)-net over F₂₇	[i]
81	Digital (31, 37, 5592430)-net over F₂₇	[i]
82	Digital (32, 38, 5593159)-net over F₂₇	[i]
83	Digital (33, 39, 5612842)-net over F₂₇	[i]
84	Digital (34, 40, 6144283)-net over F₂₇	[i]