MinT - Information on Result #1179512

Information on Result #1179512

Digital (30, 34, large)-net over F₇, using net defined by OOA based on linear OOA(7³⁴, large, F₇, 4, 4), using

appending kth column [i] based on linear OOA(7³⁴, large, F₇, 3, 4), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7², 8, F₇, 3, 2) (dual of [(8, 3), 22, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;22,7) [i]
  2. linear OOA(7³², 8388602, F₇, 3, 4) (dual of [(8388602, 3), 25165774, 5]-NRT-code), using
    - trace code [i] based on linear OOA(49¹⁶, 4194301, F₄₉, 3, 4) (dual of [(4194301, 3), 12582887, 5]-NRT-code), using
      - OA 2-folding and stacking [i] based on linear OA(49¹⁶, 8388602, F₄₉, 4) (dual of [8388602, 8388586, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(49¹⁶, large, F₄₉, 4) (dual of [large, large−16, 5]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 25679568Â | 49⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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 (31, 34, large)-net over F₇	[i]		t-Expansion
2	Digital (31, 35, large)-net over F₇	[i]		Net Duplication
3	Digital (32, 36, large)-net over F₇	[i]
4	Digital (33, 37, large)-net over F₇	[i]
5	Digital (34, 38, large)-net over F₇	[i]
6	Digital (35, 39, large)-net over F₇	[i]
7	Digital (36, 40, large)-net over F₇	[i]
8	Digital (37, 41, large)-net over F₇	[i]
9	Digital (30, 33, large)-net over F₇	[i]		m-Reduction