MinT - Information on Result #3225748

Information on Result #3225748

Digital (69, 74, large)-net over F₇, using t-expansion based on digital (67, 74, large)-net over F₇, using

trace code for nets [i] based on digital (30, 37, 5764802)-net over F₄₉, using
- net defined by OOA [i] based on linear OOA(49³⁷, 5764802, F₄₉, 9, 7) (dual of [(5764802, 9), 51883181, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(49³⁷, 5764803, F₄₉, 3, 7) (dual of [(5764803, 3), 17294372, 8]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(49⁵, 1921601, F₄₉, 3, 2) (dual of [(1921601, 3), 5764798, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(49⁵, 5884901, F₄₉, 3, 2) (dual of [(5884901, 3), 17654698, 3]-NRT-code), using
        appending 1 arbitrary column [i] based on linear OOA(49⁵, 5884901, F₄₉, 2, 2) (dual of [(5884901, 2), 11769797, 3]-NRT-code), using
        appending kth column [i] based on linear OA(49⁵, 5884901, F₄₉, 2) (dual of [5884901, 5884896, 3]-code), using
        Hamming code H(5,49) [i]
      2. linear OOA(49⁷, 1921601, F₄₉, 3, 3) (dual of [(1921601, 3), 5764796, 4]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(49⁷, 5769602, F₄₉, 3, 3) (dual of [(5769602, 3), 17308799, 4]-NRT-code), using
        OOA stacking with additional row [i] based on linear OA(49⁷, 5769603, F₄₉, 3) (dual of [5769603, 5769596, 4]-code or 5769603-cap in PG(6,49)), using
        product of two caps with tangent hyperplane [i]
      3. linear OOA(49²⁵, 1921601, F₄₉, 3, 7) (dual of [(1921601, 3), 5764778, 8]-NRT-code), using
        OOA 3-folding [i] based on linear OA(49²⁵, 5764803, F₄₉, 7) (dual of [5764803, 5764778, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(49²⁵, 5764805, F₄₉, 7) (dual of [5764805, 5764780, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(49²⁵, 5764801, F₄₉, 7) (dual of [5764801, 5764776, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(49²¹, 5764801, F₄₉, 6) (dual of [5764801, 5764780, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (70, 75, large)-net over F₇	[i]	Net Duplication
2	Digital (71, 76, large)-net over F₇	[i]
3	Digital (72, 77, large)-net over F₇	[i]
4	Digital (73, 78, large)-net over F₇	[i]
5	Digital (74, 79, large)-net over F₇	[i]
6	Digital (75, 80, large)-net over F₇	[i]
7	Digital (76, 81, large)-net over F₇	[i]
8	Digital (77, 82, large)-net over F₇	[i]
9	Digital (78, 83, large)-net over F₇	[i]
10	Digital (79, 84, large)-net over F₇	[i]
11	Digital (80, 85, large)-net over F₇	[i]
12	Digital (81, 86, large)-net over F₇	[i]
13	Digital (82, 87, large)-net over F₇	[i]
14	Digital (83, 88, large)-net over F₇	[i]