MinT - Information on Result #3222206

Information on Result #3222206

Digital (42, 46, large)-net over F₅, using t-expansion based on digital (41, 46, large)-net over F₅, using

trace code for nets [i] 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 (43, 47, large)-net over F₅	[i]		Net Duplication
2	Digital (44, 48, large)-net over F₅	[i]
3	Digital (45, 49, large)-net over F₅	[i]
4	Digital (46, 50, large)-net over F₅	[i]
5	Digital (47, 51, large)-net over F₅	[i]
6	Digital (48, 52, large)-net over F₅	[i]
7	Digital (49, 53, large)-net over F₅	[i]
8	Digital (50, 54, large)-net over F₅	[i]
9	Digital (51, 55, large)-net over F₅	[i]
10	Digital (52, 56, large)-net over F₅	[i]
11	Digital (53, 57, large)-net over F₅	[i]
12	Digital (54, 58, large)-net over F₅	[i]
13	Digital (55, 59, large)-net over F₅	[i]
14	Digital (56, 60, large)-net over F₅	[i]
15	Digital (57, 61, large)-net over F₅	[i]
16	Digital (58, 62, large)-net over F₅	[i]
17	Digital (59, 63, large)-net over F₅	[i]
18	Digital (60, 64, large)-net over F₅	[i]