MinT - Information on Result #1205319

Information on Result #1205319

Digital (41, 46, large)-net over F₅, using trace code for nets based on digital (18, 23, 4194326)-net over F₂₅, using

net defined by OOA [i] based on linear OOA(25²³, 4194326, F₂₅, 6, 5) (dual of [(4194326, 6), 25165933, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25²³, 4194327, F₂₅, 2, 5) (dual of [(4194327, 2), 8388631, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(25², 26, F₂₅, 2, 2) (dual of [(26, 2), 50, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;50,25) [i]
    2. linear OOA(25²¹, 4194301, F₂₅, 2, 5) (dual of [(4194301, 2), 8388581, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(25²¹, 8388602, F₂₅, 5) (dual of [8388602, 8388581, 6]-code), using
        discarding factors / shortening the dual code 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]

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 (42, 46, large)-net over F₅	[i]		t-Expansion
2	Digital (43, 46, large)-net over F₅	[i]		t-Expansion
3	Digital (42, 47, large)-net over F₅	[i]		Net Duplication
4	Digital (43, 48, large)-net over F₅	[i]
5	Digital (44, 49, large)-net over F₅	[i]
6	Digital (45, 50, large)-net over F₅	[i]
7	Digital (46, 51, large)-net over F₅	[i]
8	Digital (47, 52, large)-net over F₅	[i]
9	Digital (48, 53, large)-net over F₅	[i]
10	Digital (49, 54, large)-net over F₅	[i]
11	Digital (50, 55, large)-net over F₅	[i]
12	Digital (51, 56, large)-net over F₅	[i]
13	Digital (52, 57, large)-net over F₅	[i]
14	Digital (53, 58, large)-net over F₅	[i]
15	Digital (54, 59, large)-net over F₅	[i]
16	Digital (55, 60, large)-net over F₅	[i]
17	Digital (56, 61, large)-net over F₅	[i]
18	Digital (57, 62, large)-net over F₅	[i]
19	Digital (58, 63, large)-net over F₅	[i]
20	Digital (59, 64, large)-net over F₅	[i]
21	Digital (60, 65, large)-net over F₅	[i]
22	Digital (41, 45, large)-net over F₅	[i]		m-Reduction
23	Digital (41, 44, large)-net over F₅	[i]		m-Reduction