MinT - Information on Result #1220963

Information on Result #1220963

Digital (68, 77, large)-net over F₂₅, using (u,Â u+v)-construction based on

digital (12, 16, 4194301)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25¹⁶, 4194301, F₂₅, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(25¹⁶, 8388602, F₂₅, 4) (dual of [8388602, 8388586, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹⁶, large, F₂₅, 4) (dual of [large, large−16, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
digital (52, 61, 4194352)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (12, 16, 4194301)-net over F₂₅ (see above)
  2. digital (36, 45, 2097176)-net over F₂₅, using
    - (u,Â u+v)-construction [i] based on
      1. digital (0, 4, 26)-net over F₂₅, using
        net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
        Niederreiter sequence [i]
      2. digital (32, 41, 2097150)-net over F₂₅, using
        net defined by OOA [i] based on linear OOA(25⁴¹, 2097150, F₂₅, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
        OOA 4-folding and stacking with additional row [i] based on linear OA(25⁴¹, 8388601, F₂₅, 9) (dual of [8388601, 8388560, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁴¹, large, F₂₅, 9) (dual of [large, large−41, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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		Method
1	Digital (69, 77, large)-net over F₂₅	[i]	t-Expansion
2	Digital (70, 77, large)-net over F₂₅	[i]
3	Digital (71, 77, large)-net over F₂₅	[i]
4	Digital (72, 77, large)-net over F₂₅	[i]
5	Digital (73, 77, large)-net over F₂₅	[i]
6	Digital (74, 77, large)-net over F₂₅	[i]
7	Digital (69, 78, large)-net over F₂₅	[i]	Net Duplication
8	Digital (70, 79, large)-net over F₂₅	[i]
9	Digital (71, 80, large)-net over F₂₅	[i]
10	Digital (72, 81, large)-net over F₂₅	[i]
11	Digital (73, 82, large)-net over F₂₅	[i]
12	Digital (74, 83, large)-net over F₂₅	[i]
13	Digital (75, 84, large)-net over F₂₅	[i]
14	Digital (76, 85, large)-net over F₂₅	[i]
15	Digital (77, 86, large)-net over F₂₅	[i]
16	Digital (78, 87, large)-net over F₂₅	[i]
17	Digital (68, 76, large)-net over F₂₅	[i]	m-Reduction
18	Digital (68, 75, large)-net over F₂₅	[i]
19	Digital (68, 74, large)-net over F₂₅	[i]
20	Digital (68, 73, large)-net over F₂₅	[i]
21	Digital (68, 72, large)-net over F₂₅	[i]
22	Digital (68, 71, large)-net over F₂₅	[i]