MinT - Information on Result #1179422

Information on Result #1179422

Digital (81, 87, large)-net over F₃, using net defined by OOA based on linear OOA(3⁸⁷, large, F₃, 6, 6), using

appending kth column [i] based on linear OOA(3⁸⁷, large, F₃, 5, 6), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3³, 4, F₃, 5, 3) (dual of [(4, 5), 17, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(5;17,3) [i]
  2. linear OOA(3⁸⁴, 8388602, F₃, 5, 6) (dual of [(8388602, 5), 41942926, 7]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(3⁸⁴, large, F₃, 3, 6), using
      - trace code [i] based on linear OOA(81²¹, 2796201, F₈₁, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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		This result only	Method
1	Digital (82, 87, large)-net over F₃	[i]		t-Expansion
2	Digital (83, 87, large)-net over F₃	[i]
3	Digital (84, 87, large)-net over F₃	[i]
4	Digital (82, 88, large)-net over F₃	[i]		Net Duplication
5	Digital (83, 89, large)-net over F₃	[i]
6	Digital (84, 90, large)-net over F₃	[i]
7	Digital (85, 91, large)-net over F₃	[i]
8	Digital (86, 92, large)-net over F₃	[i]
9	Digital (87, 93, large)-net over F₃	[i]
10	Digital (88, 94, large)-net over F₃	[i]
11	Digital (81, 86, large)-net over F₃	[i]		m-Reduction
12	Digital (81, 85, large)-net over F₃	[i]
13	Digital (81, 84, large)-net over F₃	[i]