MinT - Information on Result #1205189

Information on Result #1205189

Digital (206, 216, large)-net over F₃, using trace code for nets based on digital (44, 54, 2796200)-net over F₈₁, using

net defined by OOA [i] based on linear OOA(81⁵⁴, 2796200, F₈₁, 14, 10) (dual of [(2796200, 14), 39146746, 11]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(81⁵⁴, 8388601, F₈₁, 2, 10) (dual of [(8388601, 2), 16777148, 11]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(81⁵⁴, 8388602, F₈₁, 2, 10) (dual of [(8388602, 2), 16777150, 11]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(81¹⁷, 4194301, F₈₁, 2, 5) (dual of [(4194301, 2), 8388585, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81¹⁷, 8388602, F₈₁, 5) (dual of [8388602, 8388585, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹⁷, large, F₈₁, 5) (dual of [large, large−17, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      2. linear OOA(81³⁷, 4194301, F₈₁, 2, 10) (dual of [(4194301, 2), 8388565, 11]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81³⁷, 8388602, F₈₁, 10) (dual of [8388602, 8388565, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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		Method
1	Digital (207, 216, large)-net over F₃	[i]	t-Expansion
2	Digital (208, 216, large)-net over F₃	[i]
3	Digital (209, 216, large)-net over F₃	[i]
4	Digital (210, 216, large)-net over F₃	[i]
5	Digital (211, 216, large)-net over F₃	[i]
6	Digital (212, 216, large)-net over F₃	[i]
7	Digital (213, 216, large)-net over F₃	[i]
8	Digital (207, 217, large)-net over F₃	[i]	Net Duplication
9	Digital (208, 218, large)-net over F₃	[i]
10	Digital (209, 219, large)-net over F₃	[i]
11	Digital (210, 220, large)-net over F₃	[i]
12	Digital (211, 221, large)-net over F₃	[i]
13	Digital (212, 222, large)-net over F₃	[i]
14	Digital (213, 223, large)-net over F₃	[i]
15	Digital (214, 224, large)-net over F₃	[i]
16	Digital (215, 225, large)-net over F₃	[i]
17	Digital (216, 226, large)-net over F₃	[i]
18	Digital (217, 227, large)-net over F₃	[i]
19	Digital (218, 228, large)-net over F₃	[i]
20	Digital (219, 229, large)-net over F₃	[i]
21	Digital (220, 230, large)-net over F₃	[i]
22	Digital (206, 215, large)-net over F₃	[i]	m-Reduction
23	Digital (206, 214, large)-net over F₃	[i]
24	Digital (206, 213, large)-net over F₃	[i]
25	Digital (206, 212, large)-net over F₃	[i]
26	Digital (206, 211, large)-net over F₃	[i]
27	Digital (206, 210, large)-net over F₃	[i]
28	Digital (206, 209, large)-net over F₃	[i]