MinT - Information on Result #1205234

Information on Result #1205234

Digital (172, 183, large)-net over F₄, using trace code for nets based on digital (50, 61, 2796233)-net over F₆₄, using

net defined by OOA [i] based on linear OOA(64⁶¹, 2796233, F₆₄, 15, 11) (dual of [(2796233, 15), 41943434, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁶¹, 5592467, F₆₄, 3, 11) (dual of [(5592467, 3), 16777340, 12]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(64³, 65, F₆₄, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;192,64) [i]
    2. linear OOA(64¹⁷, 2796201, F₆₄, 3, 5) (dual of [(2796201, 3), 8388586, 6]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(64¹⁷, 4194301, F₆₄, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(64¹⁷, large, F₆₄, 5) (dual of [large, large−17, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
    3. linear OOA(64⁴¹, 2796201, F₆₄, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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 (173, 183, large)-net over F₄	[i]	t-Expansion
2	Digital (174, 183, large)-net over F₄	[i]
3	Digital (175, 183, large)-net over F₄	[i]
4	Digital (173, 184, large)-net over F₄	[i]	Net Duplication
5	Digital (174, 185, large)-net over F₄	[i]
6	Digital (175, 186, large)-net over F₄	[i]
7	Digital (172, 182, large)-net over F₄	[i]	m-Reduction
8	Digital (172, 181, large)-net over F₄	[i]
9	Digital (172, 180, large)-net over F₄	[i]
10	Digital (172, 179, large)-net over F₄	[i]
11	Digital (172, 178, large)-net over F₄	[i]
12	Digital (172, 177, large)-net over F₄	[i]
13	Digital (172, 176, large)-net over F₄	[i]
14	Digital (172, 175, large)-net over F₄	[i]