MinT - Information on Result #1207818

Information on Result #1207818

Digital (89, 96, large)-net over F₃, using (u,Â u+v)-construction based on

digital (0, 3, 4)-net over F₃, using
- net from sequence [i] based on digital (0, 3)-sequence over F₃, using
  - Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 0 and N(F) ≥ 4, using
    - the rational function field F₃(x) [i]
  - Niederreiter sequence [i]
digital (86, 93, 8388600)-net over F₃, using
- trace code for nets [i] based on digital (24, 31, 2796200)-net over F₂₇, using
  - net defined by OOA [i] based on linear OOA(27³¹, 2796200, F₂₇, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OA(27³¹, 8388601, F₂₇, 7) (dual of [8388601, 8388570, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(27³¹, large, F₂₇, 7) (dual of [large, large−31, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [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		This result only	Method
1	Digital (90, 96, large)-net over F₃	[i]		t-Expansion
2	Digital (91, 96, large)-net over F₃	[i]
3	Digital (92, 96, large)-net over F₃	[i]
4	Digital (90, 97, large)-net over F₃	[i]		Net Duplication
5	Digital (91, 98, large)-net over F₃	[i]
6	Digital (92, 99, large)-net over F₃	[i]
7	Digital (89, 95, large)-net over F₃	[i]		m-Reduction
8	Digital (89, 94, large)-net over F₃	[i]
9	Digital (89, 93, large)-net over F₃	[i]
10	Digital (89, 92, large)-net over F₃	[i]
11	Linear OOA(3⁹⁶, large, F₃, 4, 7)	[i]		Extracting Embedded OOA
12	Linear OOA(3⁹⁶, large, F₃, 5, 7)	[i]		Extracting Embedded OOA