MinT - Information on Result #1191268

Information on Result #1191268

Digital (57, 66, 4194300)-net over F₈, using net defined by OOA based on linear OOA(8⁶⁶, 4194300, F₈, 10, 9) (dual of [(4194300, 10), 41942934, 10]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(8⁶⁶, 8388601, F₈, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁶⁶, 8388602, F₈, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
  - trace code [i] based on linear OOA(64³³, 4194301, F₆₄, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(64³³, 8388602, F₆₄, 9) (dual of [8388602, 8388569, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(64³³, large, F₆₄, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (58, 67, 4194300)-net over F₈	[i]	Net Duplication
2	Digital (61, 70, 4194309)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
3	Digital (62, 71, 4194314)-net over F₈	[i]
4	Digital (63, 72, 4194328)-net over F₈	[i]
5	Digital (64, 73, 4194365)-net over F₈	[i]
6	Digital (65, 74, 4194430)-net over F₈	[i]
7	Digital (67, 76, 4194558)-net over F₈	[i]
8	Digital (68, 77, 4196316)-net over F₈	[i]
9	Digital (69, 78, 4198332)-net over F₈	[i]
10	Digital (71, 80, 4198398)-net over F₈	[i]
11	Digital (72, 81, 4198405)-net over F₈	[i]
12	Digital (73, 82, 4210686)-net over F₈	[i]
13	Digital (74, 83, 4210690)-net over F₈	[i]
14	Digital (75, 84, 4210695)-net over F₈	[i]
15	Digital (76, 85, 4325375)-net over F₈	[i]
16	Digital (77, 86, 4456447)-net over F₈	[i]
17	Digital (79, 88, 5242879)-net over F₈	[i]
18	Digital (80, 89, 5242884)-net over F₈	[i]
19	Digital (81, 90, 5242888)-net over F₈	[i]
20	Digital (82, 91, 8388600)-net over F₈	[i]
21	Digital (72, 81, 4198460)-net over F₈	[i]
22	(67, 76, 4194796)-net in base 8	[i]
23	(71, 80, 4210556)-net in base 8	[i]
24	(72, 81, 4226940)-net in base 8	[i]
25	(73, 82, 4259580)-net in base 8	[i]
26	(75, 84, 4259589)-net in base 8	[i]
27	(81, 90, 6291455)-net in base 8	[i]
28	Digital (85, 94, large)-net over F₈	[i]	Generalized (u,Â u+v)-Construction for Nets