MinT - Information on Result #1220890

Information on Result #1220890

Digital (42, 49, large)-net over F₂₅, using (u,Â u+v)-construction based on

digital (6, 9, large)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁹, large, F₂₅, 3, 3), using
  - appending kth column [i] based on linear OOA(25⁹, large, F₂₅, 2, 3), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(25⁹, large, F₂₅, 3) (dual of [large, large−9, 4]-code), using
      - product of projective cap with (hyper)oval [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 (33, 40, 5592400)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 9, large)-net over F₂₅ (see above)
  2. digital (24, 31, 2796200)-net over F₂₅, using
    - net defined by OOA [i] based on linear OOA(25³¹, 2796200, F₂₅, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
      - OOA 3-folding and stacking with additional row [i] based on linear OA(25³¹, 8388601, F₂₅, 7) (dual of [8388601, 8388570, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(25³¹, large, F₂₅, 7) (dual of [large, large−31, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’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 (43, 49, large)-net over F₂₅	[i]		t-Expansion
2	Digital (44, 49, large)-net over F₂₅	[i]
3	Digital (45, 49, large)-net over F₂₅	[i]
4	Digital (46, 49, large)-net over F₂₅	[i]
5	Digital (43, 50, large)-net over F₂₅	[i]		Net Duplication
6	Digital (44, 51, large)-net over F₂₅	[i]
7	Digital (45, 52, large)-net over F₂₅	[i]
8	Digital (46, 53, large)-net over F₂₅	[i]
9	Digital (47, 54, large)-net over F₂₅	[i]
10	Digital (48, 55, large)-net over F₂₅	[i]
11	Digital (49, 56, large)-net over F₂₅	[i]
12	Digital (50, 57, large)-net over F₂₅	[i]
13	Digital (51, 58, large)-net over F₂₅	[i]
14	Digital (52, 59, large)-net over F₂₅	[i]
15	Digital (53, 60, large)-net over F₂₅	[i]
16	Digital (54, 61, large)-net over F₂₅	[i]
17	Digital (55, 62, large)-net over F₂₅	[i]
18	Digital (56, 63, large)-net over F₂₅	[i]
19	Digital (42, 48, large)-net over F₂₅	[i]		m-Reduction
20	Digital (42, 47, large)-net over F₂₅	[i]
21	Digital (42, 46, large)-net over F₂₅	[i]
22	Digital (42, 45, large)-net over F₂₅	[i]