MinT - Information on Result #1179710

Information on Result #1179710

Digital (7, 12, 32513)-net over F₁₂₈, using net defined by OOA based on linear OOA(128¹², 32513, F₁₂₈, 5, 5) (dual of [(32513, 5), 162553, 6]-NRT-code), using

appending kth column [i] based on linear OOA(128¹², 32513, F₁₂₈, 4, 5) (dual of [(32513, 4), 130040, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(128¹², 65027, F₁₂₈, 5) (dual of [65027, 65015, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(128¹², 65028, F₁₂₈, 5) (dual of [65028, 65016, 6]-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OA(128¹, 16257, F₁₂₈, 1) (dual of [16257, 16256, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OA(128¹, 16257, F₁₂₈, 1) (dual of [16257, 16256, 2]-code) (see above)
      3. linear OA(128³, 16257, F₁₂₈, 2) (dual of [16257, 16254, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
        Hamming code H(3,128) [i]
      4. linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (39, 49, 1710233)-net over F₁₂₈	[i]	(u,Â u+v)-Construction for Nets
2	Digital (42, 53, 1710233)-net over F₁₂₈	[i]	(u,Â u+v)-Construction for Nets
3	Digital (51, 62, 4548581)-net over F₁₂₈	[i]	Generalized (u,Â u+v)-Construction for Nets
4	Digital (48, 58, 4548582)-net over F₁₂₈	[i]	Generalized (u,Â u+v)-Construction for Nets