MinT - Information on Result #3244337

Information on Result #3244337

Digital (23, 27, large)-net over F₄₉, using t-expansion based on digital (22, 27, large)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 5, 5884901)-net over F₄₉, using
  - kÂ =Â 2 construction [i]
2. digital (17, 22, 5764804)-net over F₄₉, using
  - (u,Â u+v)-construction [i] based on
    1. digital (3, 5, 5884901)-net over F₄₉ (see above)
    2. digital (12, 17, 2882402)-net over F₄₉, using
      - net defined by OOA [i] based on linear OOA(49¹⁷, 2882402, F₄₉, 5, 5) (dual of [(2882402, 5), 14411993, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] 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 (24, 28, large)-net over F₄₉	[i]	Net Duplication
2	Digital (25, 29, large)-net over F₄₉	[i]
3	Digital (26, 30, large)-net over F₄₉	[i]
4	Digital (27, 31, large)-net over F₄₉	[i]
5	Digital (28, 32, large)-net over F₄₉	[i]