MinT - Information on Result #1179028

Information on Result #1179028

Digital (10, 13, 6120101)-net over F₇, using net defined by OOA based on linear OOA(7¹³, 6120101, F₇, 3, 3) (dual of [(6120101, 3), 18360290, 4]-NRT-code), using

appending kth column [i] based on linear OOA(7¹³, 6120101, F₇, 2, 3) (dual of [(6120101, 2), 12240189, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7¹³, 6120101, F₇, 3) (dual of [6120101, 6120088, 4]-code or 6120101-cap in PG(12,7)), using
  - product of projective cap with cap in AG(6,Â 7) [i] based on linear OA(7⁷, 2499, F₇, 3) (dual of [2499, 2492, 4]-code or 2499-cap in PG(6,7)), using
    - product of two caps with tangent hyperplane [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 (49, 55, 7686404)-net over F₇	[i]	(u,Â u+v)-Construction for Nets
2	Digital (51, 57, 7686412)-net over F₇	[i]
3	Digital (59, 65, large)-net over F₇	[i]
4	Digital (56, 63, 7686404)-net over F₇	[i]
5	Digital (98, 107, large)-net over F₇	[i]	Generalized (u,Â u+v)-Construction for Nets
6	Digital (66, 73, large)-net over F₇	[i]
7	Digital (97, 106, large)-net over F₇	[i]
8	Digital (65, 72, large)-net over F₇	[i]
9	Digital (58, 64, large)-net over F₇	[i]
10	Digital (93, 102, 6291450)-net over F₇	[i]
11	Digital (95, 104, large)-net over F₇	[i]
12	Digital (59, 66, 7686461)-net over F₇	[i]
13	Digital (60, 67, 7686804)-net over F₇	[i]
14	Digital (61, 68, 7689205)-net over F₇	[i]
15	Digital (62, 69, 7706012)-net over F₇	[i]
16	Digital (63, 70, 7823661)-net over F₇	[i]
17	Digital (64, 71, large)-net over F₇	[i]
18	Digital (52, 58, 7686461)-net over F₇	[i]
19	Digital (53, 59, 7686804)-net over F₇	[i]
20	Digital (54, 60, 7689205)-net over F₇	[i]
21	Digital (55, 61, 7706012)-net over F₇	[i]
22	Digital (56, 62, 7823661)-net over F₇	[i]
23	Digital (57, 63, large)-net over F₇	[i]