MinT - Information on Result #1213207

Information on Result #1213207

Digital (70, 77, large)-net over F₅, using (u,Â u+v)-construction based on

digital (12, 15, 3050326)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹⁵, 3050326, F₅, 3, 3) (dual of [(3050326, 3), 9150963, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(5¹⁵, 3050326, F₅, 2, 3) (dual of [(3050326, 2), 6100637, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5¹⁵, 3050326, F₅, 3) (dual of [3050326, 3050311, 4]-code or 3050326-cap in PG(14,5)), using
      - product of projective cap with cap in AG(6,Â 5) [i] based on linear OA(5⁹, 4700, F₅, 3) (dual of [4700, 4691, 4]-code or 4700-cap in PG(8,5)), using
        caps completed using a computer search [i]
digital (55, 62, 5592400)-net over F₅, using
- trace code for nets [i] based on digital (24, 31, 2796200)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25³¹, 2796200, F₂₅, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OA(25³¹, 8388601, F₂₅, 7) (dual of [8388601, 8388570, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(25³¹, large, F₂₅, 7) (dual of [large, large−31, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (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		This result only	Method
1	Digital (71, 77, large)-net over F₅	[i]		t-Expansion
2	Digital (72, 77, large)-net over F₅	[i]
3	Digital (73, 77, large)-net over F₅	[i]
4	Digital (74, 77, large)-net over F₅	[i]
5	Digital (71, 78, large)-net over F₅	[i]		Net Duplication
6	Digital (72, 79, large)-net over F₅	[i]
7	Digital (73, 80, large)-net over F₅	[i]
8	Digital (74, 81, large)-net over F₅	[i]
9	Digital (75, 82, large)-net over F₅	[i]
10	Digital (76, 83, large)-net over F₅	[i]
11	Digital (77, 84, large)-net over F₅	[i]
12	Digital (78, 85, large)-net over F₅	[i]
13	Digital (79, 86, large)-net over F₅	[i]
14	Digital (80, 87, large)-net over F₅	[i]
15	Digital (81, 88, large)-net over F₅	[i]
16	Digital (82, 89, large)-net over F₅	[i]
17	Digital (83, 90, large)-net over F₅	[i]
18	Digital (84, 91, large)-net over F₅	[i]
19	Digital (85, 92, large)-net over F₅	[i]
20	Digital (86, 93, large)-net over F₅	[i]
21	Digital (87, 94, large)-net over F₅	[i]
22	Digital (88, 95, large)-net over F₅	[i]
23	Digital (89, 96, large)-net over F₅	[i]
24	Digital (90, 97, large)-net over F₅	[i]
25	Digital (91, 98, large)-net over F₅	[i]
26	Digital (92, 99, large)-net over F₅	[i]
27	Digital (93, 100, large)-net over F₅	[i]
28	Digital (94, 101, large)-net over F₅	[i]
29	Digital (95, 102, large)-net over F₅	[i]
30	Digital (96, 103, large)-net over F₅	[i]
31	Digital (70, 76, large)-net over F₅	[i]		m-Reduction
32	Digital (70, 75, large)-net over F₅	[i]
33	Digital (70, 74, large)-net over F₅	[i]
34	Digital (70, 73, large)-net over F₅	[i]