MinT - Information on Result #1205228

Information on Result #1205228

Digital (129, 138, large)-net over F₄, using trace code for nets based on digital (37, 46, 4194300)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64⁴⁶, 4194300, F₆₄, 10, 9) (dual of [(4194300, 10), 41942954, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁴⁶, 8388601, F₆₄, 2, 9) (dual of [(8388601, 2), 16777156, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴⁶, 8388602, F₆₄, 2, 9) (dual of [(8388602, 2), 16777158, 10]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(64¹³, 4194301, F₆₄, 2, 4) (dual of [(4194301, 2), 8388589, 5]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64¹³, 8388602, F₆₄, 4) (dual of [8388602, 8388589, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹³, large, F₆₄, 4) (dual of [large, large−13, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. 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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (130, 138, large)-net over F₄	[i]	t-Expansion
2	Digital (131, 138, large)-net over F₄	[i]
3	Digital (132, 138, large)-net over F₄	[i]
4	Digital (133, 138, large)-net over F₄	[i]
5	Digital (134, 138, large)-net over F₄	[i]
6	Digital (135, 138, large)-net over F₄	[i]
7	Digital (130, 139, large)-net over F₄	[i]	Net Duplication
8	Digital (131, 140, large)-net over F₄	[i]
9	Digital (132, 141, large)-net over F₄	[i]
10	Digital (133, 142, large)-net over F₄	[i]
11	Digital (134, 143, large)-net over F₄	[i]
12	Digital (135, 144, large)-net over F₄	[i]
13	Digital (129, 137, large)-net over F₄	[i]	m-Reduction
14	Digital (129, 136, large)-net over F₄	[i]
15	Digital (129, 135, large)-net over F₄	[i]
16	Digital (129, 134, large)-net over F₄	[i]
17	Digital (129, 133, large)-net over F₄	[i]
18	Digital (129, 132, large)-net over F₄	[i]