MinT - Information on Result #3176567

Information on Result #3176567

Digital (116, 128, large)-net over F₁₆, using 1 times m-reduction based on digital (116, 129, large)-net over F₁₆, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 2, 17)-net over F₁₆, using
  - kÂ =Â 2 construction [i]
2. digital (0, 3, 17)-net over F₁₆, using
  - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
      - the rational function field F₁₆(x) [i]
    - Niederreiter sequence [i]
3. digital (15, 19, 2796200)-net over F₁₆, using
  - s-reduction based on digital (15, 19, 4194301)-net over F₁₆, using
    - net defined by OOA [i] based on linear OOA(16¹⁹, 4194301, F₁₆, 4, 4) (dual of [(4194301, 4), 16777185, 5]-NRT-code), using
      - OA 2-folding and stacking [i] based on linear OA(16¹⁹, 8388602, F₁₆, 4) (dual of [8388602, 8388583, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(16¹⁹, large, F₁₆, 4) (dual of [large, large−19, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 16⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
4. digital (25, 31, 2796200)-net over F₁₆, using
  - s-reduction based on digital (25, 31, 2796201)-net over F₁₆, using
    - net defined by OOA [i] based on linear OOA(16³¹, 2796201, F₁₆, 6, 6) (dual of [(2796201, 6), 16777175, 7]-NRT-code), using
      - OA 3-folding and stacking [i] based on linear OA(16³¹, large, F₁₆, 6) (dual of [large, large−31, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 16⁶âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
5. digital (61, 74, 2796200)-net over F₁₆, using
  - net defined by OOA [i] based on linear OOA(16⁷⁴, 2796200, F₁₆, 14, 13) (dual of [(2796200, 14), 39146726, 14]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OOA(16⁷⁴, 8388601, F₁₆, 2, 13) (dual of [(8388601, 2), 16777128, 14]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(16⁷⁴, 8388602, F₁₆, 2, 13) (dual of [(8388602, 2), 16777130, 14]-NRT-code), using
        trace code [i] based on linear OOA(256³⁷, 4194301, F₂₅₆, 2, 13) (dual of [(4194301, 2), 8388565, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256³⁷, 8388602, F₂₅₆, 13) (dual of [8388602, 8388565, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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 (117, 128, large)-net over F₁₆	[i]	t-Expansion
2	Digital (118, 128, large)-net over F₁₆	[i]
3	Digital (119, 128, large)-net over F₁₆	[i]
4	Digital (120, 128, large)-net over F₁₆	[i]
5	Digital (121, 128, large)-net over F₁₆	[i]
6	Digital (122, 128, large)-net over F₁₆	[i]
7	Digital (123, 128, large)-net over F₁₆	[i]
8	Digital (124, 128, large)-net over F₁₆	[i]
9	Digital (125, 128, large)-net over F₁₆	[i]