MinT - Information on Result #1230604

Information on Result #1230604

Digital (84, 95, large)-net over F₂₅, using generalized (u,Â u+v)-construction based on

digital (0, 0, 391875)-net over F₂₅, using
- s-reduction based on digital (0, 0, s)-net over F₂₅ for arbitrarily large s, using
  - arbitrary set of 25⁰ points [i]
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 0, 391875)-net over F₂₅ (see above)
digital (0, 1, 391875)-net over F₂₅, using
- s-reduction based on digital (0, 1, s)-net over F₂₅ for arbitrarily large s, using
  - construction for strength kÂ =Â 1 [i]
digital (0, 1, 391875)-net over F₂₅ (see above)
digital (0, 1, 391875)-net over F₂₅ (see above)
digital (0, 1, 391875)-net over F₂₅ (see above)
digital (0, 1, 391875)-net over F₂₅ (see above)
digital (0, 1, 391875)-net over F₂₅ (see above)
digital (3, 5, 391875)-net over F₂₅, using
- s-reduction based on digital (3, 5, 406901)-net over F₂₅, using
  - kÂ =Â 2 construction [i]
digital (3, 5, 391875)-net over F₂₅ (see above)
digital (4, 7, 391875)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁷, 391875, F₂₅, 3, 3) (dual of [(391875, 3), 1175618, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(25⁷, 391875, F₂₅, 2, 3) (dual of [(391875, 2), 783743, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(25⁷, 391875, F₂₅, 3) (dual of [391875, 391868, 4]-code or 391875-cap in PG(6,25)), using
      - product of two caps with tangent hyperplane [i]
digital (16, 21, 1677720)-net over F₂₅, using
- s-reduction based on digital (16, 21, 4194301)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25²¹, 4194301, F₂₅, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(25²¹, large, F₂₅, 5) (dual of [large, large−21, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
digital (40, 51, 1677720)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁵¹, 1677720, F₂₅, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(25⁵¹, 8388601, F₂₅, 11) (dual of [8388601, 8388550, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(25⁵¹, large, F₂₅, 11) (dual of [large, large−51, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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 (85, 95, large)-net over F₂₅	[i]	t-Expansion
2	Digital (86, 95, large)-net over F₂₅	[i]
3	Digital (87, 95, large)-net over F₂₅	[i]
4	Digital (88, 95, large)-net over F₂₅	[i]
5	Digital (89, 95, large)-net over F₂₅	[i]
6	Digital (90, 95, large)-net over F₂₅	[i]
7	Digital (91, 95, large)-net over F₂₅	[i]
8	Digital (92, 95, large)-net over F₂₅	[i]
9	Digital (85, 96, large)-net over F₂₅	[i]	Net Duplication
10	Digital (86, 97, large)-net over F₂₅	[i]
11	Digital (87, 98, large)-net over F₂₅	[i]
12	Digital (88, 99, large)-net over F₂₅	[i]
13	Digital (89, 100, large)-net over F₂₅	[i]
14	Digital (90, 101, large)-net over F₂₅	[i]
15	Digital (91, 102, large)-net over F₂₅	[i]
16	Digital (92, 103, large)-net over F₂₅	[i]
17	Digital (93, 104, large)-net over F₂₅	[i]
18	Digital (94, 105, large)-net over F₂₅	[i]
19	Digital (95, 106, large)-net over F₂₅	[i]
20	Digital (96, 107, large)-net over F₂₅	[i]
21	Digital (97, 108, large)-net over F₂₅	[i]
22	Digital (98, 109, large)-net over F₂₅	[i]
23	Digital (99, 110, large)-net over F₂₅	[i]
24	Digital (84, 94, large)-net over F₂₅	[i]	m-Reduction
25	Digital (84, 93, large)-net over F₂₅	[i]
26	Digital (84, 92, large)-net over F₂₅	[i]
27	Digital (84, 91, large)-net over F₂₅	[i]
28	Digital (84, 90, large)-net over F₂₅	[i]
29	Digital (84, 89, large)-net over F₂₅	[i]
30	Digital (84, 88, large)-net over F₂₅	[i]
31	Digital (84, 87, large)-net over F₂₅	[i]