MinT - Information on Result #1205428

Information on Result #1205428

Digital (33, 38, large)-net over F₈, using trace code for nets based on digital (14, 19, 4194365)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64¹⁹, 4194365, F₆₄, 6, 5) (dual of [(4194365, 6), 25166171, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(64¹⁹, 4194366, F₆₄, 2, 5) (dual of [(4194366, 2), 8388713, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(64², 65, F₆₄, 2, 2) (dual of [(65, 2), 128, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;128,64) [i]
    2. linear OOA(64¹⁷, 4194301, F₆₄, 2, 5) (dual of [(4194301, 2), 8388585, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64¹⁷, 8388602, F₆₄, 5) (dual of [8388602, 8388585, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹⁷, large, F₆₄, 5) (dual of [large, large−17, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’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 (34, 38, large)-net over F₈	[i]		t-Expansion
2	Digital (35, 38, large)-net over F₈	[i]		t-Expansion
3	Digital (34, 39, large)-net over F₈	[i]		Net Duplication
4	Digital (35, 40, large)-net over F₈	[i]
5	Digital (36, 41, large)-net over F₈	[i]
6	Digital (37, 42, large)-net over F₈	[i]
7	Digital (38, 43, large)-net over F₈	[i]
8	Digital (39, 44, large)-net over F₈	[i]
9	Digital (40, 45, large)-net over F₈	[i]
10	Digital (41, 46, large)-net over F₈	[i]
11	Digital (42, 47, large)-net over F₈	[i]
12	Digital (43, 48, large)-net over F₈	[i]
13	Digital (44, 49, large)-net over F₈	[i]
14	Digital (45, 50, large)-net over F₈	[i]
15	Digital (46, 51, large)-net over F₈	[i]
16	Digital (47, 52, large)-net over F₈	[i]
17	Digital (33, 37, large)-net over F₈	[i]		m-Reduction
18	Digital (33, 36, large)-net over F₈	[i]		m-Reduction