MinT - Information on Result #1224608

Information on Result #1224608

Digital (64, 72, large)-net over F₃₂, using (u,Â u+v)-construction based on

digital (12, 16, 4194301)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32¹⁶, 4194301, F₃₂, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(32¹⁶, 8388602, F₃₂, 4) (dual of [8388602, 8388586, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(32¹⁶, large, F₃₂, 4) (dual of [large, large−16, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
digital (48, 56, 4194366)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (12, 16, 4194301)-net over F₃₂ (see above)
  2. digital (32, 40, 2097183)-net over F₃₂, using
    - (u,Â u+v)-construction [i] based on
      1. digital (0, 4, 33)-net over F₃₂, using
        net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
        Niederreiter sequence [i]
      2. digital (28, 36, 2097150)-net over F₃₂, using
        net defined by OOA [i] based on linear OOA(32³⁶, 2097150, F₃₂, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
        OA 4-folding and stacking [i] based on linear OA(32³⁶, 8388600, F₃₂, 8) (dual of [8388600, 8388564, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(32³⁶, large, F₃₂, 8) (dual of [large, large−36, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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 (65, 72, large)-net over F₃₂	[i]	t-Expansion
2	Digital (66, 72, large)-net over F₃₂	[i]
3	Digital (67, 72, large)-net over F₃₂	[i]
4	Digital (65, 73, large)-net over F₃₂	[i]	Net Duplication
5	Digital (66, 74, large)-net over F₃₂	[i]
6	Digital (67, 75, large)-net over F₃₂	[i]
7	Digital (64, 71, large)-net over F₃₂	[i]	m-Reduction
8	Digital (64, 70, large)-net over F₃₂	[i]
9	Digital (64, 69, large)-net over F₃₂	[i]
10	Digital (64, 68, large)-net over F₃₂	[i]
11	Digital (64, 67, large)-net over F₃₂	[i]