MinT - Information on Result #1179684

Information on Result #1179684

Digital (6, 11, 9721)-net over F₈₁, using net defined by OOA based on linear OOA(81¹¹, 9721, F₈₁, 5, 5) (dual of [(9721, 5), 48594, 6]-NRT-code), using

appending kth column [i] based on linear OOA(81¹¹, 9721, F₈₁, 4, 5) (dual of [(9721, 4), 38873, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(81¹¹, 19443, F₈₁, 5) (dual of [19443, 19432, 6]-code), using
  - (u,Â uâˆ’v,Â u+v+w)-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(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]
    3. 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 (38, 48, 1687441)-net over F₈₁	[i]		(u,Â u+v)-Construction for Nets
2	Digital (41, 52, 1687441)-net over F₈₁	[i]		(u,Â u+v)-Construction for Nets