MinT - Information on Result #1205292

Information on Result #1205292

Digital (199, 212, large)-net over F₄, using trace code for nets based on digital (40, 53, 2796200)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256⁵³, 2796200, F₂₅₆, 14, 13) (dual of [(2796200, 14), 39146747, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(256⁵³, 8388601, F₂₅₆, 2, 13) (dual of [(8388601, 2), 16777149, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(256⁵³, 8388602, F₂₅₆, 2, 13) (dual of [(8388602, 2), 16777151, 14]-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(256³⁷, 4194301, F₂₅₆, 2, 13) (dual of [(4194301, 2), 8388565, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256³⁷, 8388602, F₂₅₆, 13) (dual of [8388602, 8388565, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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 (200, 212, large)-net over F₄	[i]	t-Expansion
2	Digital (201, 212, large)-net over F₄	[i]
3	Digital (202, 212, large)-net over F₄	[i]
4	Digital (203, 212, large)-net over F₄	[i]
5	Digital (204, 212, large)-net over F₄	[i]
6	Digital (205, 212, large)-net over F₄	[i]
7	Digital (200, 213, large)-net over F₄	[i]	Net Duplication
8	Digital (201, 214, large)-net over F₄	[i]
9	Digital (202, 215, large)-net over F₄	[i]
10	Digital (203, 216, large)-net over F₄	[i]
11	Digital (204, 217, large)-net over F₄	[i]
12	Digital (205, 218, large)-net over F₄	[i]
13	Digital (199, 211, large)-net over F₄	[i]	m-Reduction
14	Digital (199, 210, large)-net over F₄	[i]
15	Digital (199, 209, large)-net over F₄	[i]
16	Digital (199, 208, large)-net over F₄	[i]
17	Digital (199, 207, large)-net over F₄	[i]
18	Digital (199, 206, large)-net over F₄	[i]
19	Digital (199, 205, large)-net over F₄	[i]
20	Digital (199, 204, large)-net over F₄	[i]
21	Digital (199, 203, large)-net over F₄	[i]
22	Digital (199, 202, large)-net over F₄	[i]