MinT - Information on Result #1179686

Information on Result #1179686

Digital (7, 12, 12961)-net over F₈₁, using net defined by OOA based on linear OOA(81¹², 12961, F₈₁, 5, 5) (dual of [(12961, 5), 64793, 6]-NRT-code), using

appending kth column [i] based on linear OOA(81¹², 12961, F₈₁, 4, 5) (dual of [(12961, 4), 51832, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(81¹², 25923, F₈₁, 5) (dual of [25923, 25911, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(81¹², 25924, F₈₁, 5) (dual of [25924, 25912, 6]-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OA(81¹, 6481, F₈₁, 1) (dual of [6481, 6480, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OA(81¹, 6481, F₈₁, 1) (dual of [6481, 6480, 2]-code) (see above)
      3. linear OA(81³, 6481, F₈₁, 2) (dual of [6481, 6478, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
        Hamming code H(3,81) [i]
      4. linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 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		This result only	Method
1	Digital (39, 49, 1690681)-net over F₈₁	[i]		(u,Â u+v)-Construction for Nets
2	Digital (42, 53, 1690681)-net over F₈₁	[i]		(u,Â u+v)-Construction for Nets