MinT - Information on Result #1178990

Information on Result #1178990

Digital (56, 61, large)-net over F₃, using net defined by OOA based on linear OOA(3⁶¹, large, F₃, 5, 5), using

appending kth column [i] based on linear OOA(3⁶¹, large, F₃, 4, 5), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹, 2391484, F₃, 4, 1) (dual of [(2391484, 4), 9565935, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 4, 1) for arbitrarily large s, using
      - appending 3 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(3¹⁴, 2391484, F₃, 4, 2) (dual of [(2391484, 4), 9565922, 3]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3¹⁴, 2391484, F₃, 2, 2) (dual of [(2391484, 2), 4782954, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(3¹⁴, 2391484, F₃, 2) (dual of [2391484, 2391470, 3]-code), using
        Hamming code H(14,3) [i]
  3. linear OOA(3⁴⁶, 4194301, F₃, 4, 5) (dual of [(4194301, 4), 16777158, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴⁶, large, F₃, 5) (dual of [large, large−46, 6]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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 (57, 61, large)-net over F₃	[i]		t-Expansion
2	Digital (58, 61, large)-net over F₃	[i]		t-Expansion
3	Digital (57, 62, large)-net over F₃	[i]		Net Duplication
4	Digital (58, 63, large)-net over F₃	[i]
5	Digital (59, 64, large)-net over F₃	[i]
6	Digital (60, 65, large)-net over F₃	[i]
7	Digital (61, 66, large)-net over F₃	[i]
8	Digital (62, 67, large)-net over F₃	[i]
9	Digital (63, 68, large)-net over F₃	[i]
10	Digital (64, 69, large)-net over F₃	[i]
11	Digital (65, 70, large)-net over F₃	[i]
12	Digital (66, 71, large)-net over F₃	[i]
13	Digital (67, 72, large)-net over F₃	[i]
14	Digital (68, 73, large)-net over F₃	[i]
15	Digital (69, 74, large)-net over F₃	[i]
16	Digital (70, 75, large)-net over F₃	[i]
17	Digital (71, 76, large)-net over F₃	[i]
18	Digital (56, 60, large)-net over F₃	[i]		m-Reduction
19	Digital (56, 59, large)-net over F₃	[i]		m-Reduction