MinT - Information on Result #1179320

Information on Result #1179320

Digital (155, 164, large)-net over F₂, using net defined by OOA based on linear OOA(2¹⁶⁴, large, F₂, 9, 9), using

appending kth column [i] based on linear OOA(2¹⁶⁴, large, F₂, 8, 9), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴⁴, 4194305, F₂, 8, 4) (dual of [(4194305, 8), 33554396, 5]-NRT-code), using
    - appending 4 arbitrary columns [i] based on linear OOA(2⁴⁴, 4194305, F₂, 4, 4) (dual of [(4194305, 4), 16777176, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(2⁴⁴, 4194305, F₂, 3, 4) (dual of [(4194305, 3), 12582871, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (40, 44, 4194305)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(2¹²⁰, 4194304, F₂, 8, 9) (dual of [(4194304, 8), 33554312, 10]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁴, 3, F₂, 8, 4) (dual of [(3, 8), 20, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(8;20,2) [i]
      2. linear OOA(2¹¹⁶, 4194301, F₂, 8, 9) (dual of [(4194301, 8), 33554292, 10]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹¹⁶, large, F₂, 2, 9), using
        OOAs constructed from BCH codes [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 (156, 164, large)-net over F₂	[i]		t-Expansion
2	Digital (157, 164, large)-net over F₂	[i]
3	Digital (158, 164, large)-net over F₂	[i]
4	Digital (159, 164, large)-net over F₂	[i]
5	Digital (160, 164, large)-net over F₂	[i]
6	Digital (161, 164, large)-net over F₂	[i]
7	Digital (156, 165, large)-net over F₂	[i]		Net Duplication
8	Digital (157, 166, large)-net over F₂	[i]
9	Digital (158, 167, large)-net over F₂	[i]
10	Digital (159, 168, large)-net over F₂	[i]
11	Digital (160, 169, large)-net over F₂	[i]
12	Digital (161, 170, large)-net over F₂	[i]
13	Digital (162, 171, large)-net over F₂	[i]
14	Digital (163, 172, large)-net over F₂	[i]
15	Digital (164, 173, large)-net over F₂	[i]
16	Digital (165, 174, large)-net over F₂	[i]
17	Digital (166, 175, large)-net over F₂	[i]
18	Digital (167, 176, large)-net over F₂	[i]
19	Digital (168, 177, large)-net over F₂	[i]
20	Digital (169, 178, large)-net over F₂	[i]
21	Digital (170, 179, large)-net over F₂	[i]
22	Digital (171, 180, large)-net over F₂	[i]
23	Digital (172, 181, large)-net over F₂	[i]
24	Digital (173, 182, large)-net over F₂	[i]
25	Digital (174, 183, large)-net over F₂	[i]
26	Digital (175, 184, large)-net over F₂	[i]
27	Digital (176, 185, large)-net over F₂	[i]
28	Digital (177, 186, large)-net over F₂	[i]
29	Digital (178, 187, large)-net over F₂	[i]
30	Digital (179, 188, large)-net over F₂	[i]