MinT - Information on Result #1205287

Information on Result #1205287

Digital (188, 200, large)-net over F₄, using trace code for nets based on digital (38, 50, 2796200)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256⁵⁰, 2796200, F₂₅₆, 14, 12) (dual of [(2796200, 14), 39146750, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(256⁵⁰, 8388601, F₂₅₆, 2, 12) (dual of [(8388601, 2), 16777152, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(256⁵⁰, 8388602, F₂₅₆, 2, 12) (dual of [(8388602, 2), 16777154, 13]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(256¹⁶, 4194301, F₂₅₆, 2, 6) (dual of [(4194301, 2), 8388586, 7]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256¹⁶, 8388602, F₂₅₆, 6) (dual of [8388602, 8388586, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹⁶, large, F₂₅₆, 6) (dual of [large, large−16, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OOA(256³⁴, 4194301, F₂₅₆, 2, 12) (dual of [(4194301, 2), 8388568, 13]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256³⁴, 8388602, F₂₅₆, 12) (dual of [8388602, 8388568, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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 (189, 200, large)-net over F₄	[i]	t-Expansion
2	Digital (190, 200, large)-net over F₄	[i]
3	Digital (191, 200, large)-net over F₄	[i]
4	Digital (192, 200, large)-net over F₄	[i]
5	Digital (193, 200, large)-net over F₄	[i]
6	Digital (194, 200, large)-net over F₄	[i]
7	Digital (189, 201, large)-net over F₄	[i]	Net Duplication
8	Digital (190, 202, large)-net over F₄	[i]
9	Digital (191, 203, large)-net over F₄	[i]
10	Digital (192, 204, large)-net over F₄	[i]
11	Digital (193, 205, large)-net over F₄	[i]
12	Digital (194, 206, large)-net over F₄	[i]
13	Digital (188, 199, large)-net over F₄	[i]	m-Reduction
14	Digital (188, 198, large)-net over F₄	[i]
15	Digital (188, 197, large)-net over F₄	[i]
16	Digital (188, 196, large)-net over F₄	[i]
17	Digital (188, 195, large)-net over F₄	[i]
18	Digital (188, 194, large)-net over F₄	[i]
19	Digital (188, 193, large)-net over F₄	[i]
20	Digital (188, 192, large)-net over F₄	[i]
21	Digital (188, 191, large)-net over F₄	[i]