MinT - Information on Result #3225610

Information on Result #3225610

Digital (41, 44, large)-net over F₇, using t-expansion based on digital (39, 44, large)-net over F₇, using

trace code for nets [i] based on digital (17, 22, 5764803)-net over F₄₉, using
- net defined by OOA [i] based on linear OOA(49²², 5764803, F₄₉, 6, 5) (dual of [(5764803, 6), 34588796, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(49²², 5764804, F₄₉, 2, 5) (dual of [(5764804, 2), 11529586, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. 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(49¹⁷, 2882402, F₄₉, 2, 5) (dual of [(2882402, 2), 5764787, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(49¹⁷, 5764804, F₄₉, 5) (dual of [5764804, 5764787, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(49¹⁷, 5764805, F₄₉, 5) (dual of [5764805, 5764788, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(49¹⁷, 5764801, F₄₉, 5) (dual of [5764801, 5764784, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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 (42, 45, large)-net over F₇	[i]	Net Duplication
2	Digital (43, 46, large)-net over F₇	[i]
3	Digital (44, 47, large)-net over F₇	[i]
4	Digital (45, 48, large)-net over F₇	[i]
5	Digital (46, 49, large)-net over F₇	[i]
6	Digital (47, 50, large)-net over F₇	[i]
7	Digital (48, 51, large)-net over F₇	[i]
8	Digital (49, 52, large)-net over F₇	[i]
9	Digital (50, 53, large)-net over F₇	[i]
10	Digital (51, 54, large)-net over F₇	[i]
11	Digital (52, 55, large)-net over F₇	[i]
12	Digital (53, 56, large)-net over F₇	[i]
13	Digital (54, 57, large)-net over F₇	[i]
14	Digital (55, 58, large)-net over F₇	[i]
15	Digital (56, 59, large)-net over F₇	[i]