MinT - Information on Result #1193022

Information on Result #1193022

Digital (24, 29, 2391487)-net over F₉, using net defined by OOA based on linear OOA(9²⁹, 2391487, F₉, 5, 5) (dual of [(2391487, 5), 11957406, 6]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OA(9²⁹, 4782975, F₉, 5) (dual of [4782975, 4782946, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(9²⁹, 4782976, F₉, 5) (dual of [4782976, 4782947, 6]-code), using
  - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
    1. linear OA(9²⁹, 4782969, F₉, 5) (dual of [4782969, 4782940, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OA(9²², 4782969, F₉, 4) (dual of [4782969, 4782947, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (89, 99, 3355460)-net over F₉	[i]	(u,Â u+v)-Construction for Nets
2	Digital (90, 100, 3355472)-net over F₉	[i]
3	Digital (91, 101, 3355512)-net over F₉	[i]
4	Digital (93, 103, 5746927)-net over F₉	[i]
5	Digital (96, 107, 3355460)-net over F₉	[i]
6	Digital (97, 108, 3355472)-net over F₉	[i]
7	Digital (98, 109, 3355512)-net over F₉	[i]
8	Digital (100, 111, 5746927)-net over F₉	[i]
9	Digital (112, 123, 6815735)-net over F₉	[i]	Generalized (u,Â u+v)-Construction for Nets
10	Digital (113, 124, large)-net over F₉	[i]
11	Digital (106, 116, 6815727)-net over F₉	[i]
12	Digital (107, 117, large)-net over F₉	[i]
13	Digital (112, 123, 7652760)-net over F₉	[i]
14	Digital (106, 116, 7652744)-net over F₉	[i]
15	Digital (111, 122, 7158757)-net over F₉	[i]
16	Digital (112, 123, 8138414)-net over F₉	[i]
17	Digital (104, 114, 7158757)-net over F₉	[i]
18	Digital (105, 115, 8138414)-net over F₉	[i]