MinT - Information on Result #1200852

Information on Result #1200852

Digital (7, 12, 8065)-net over F₆₄, using net defined by OOA based on linear OOA(64¹², 8065, F₆₄, 5, 5) (dual of [(8065, 5), 40313, 6]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OA(64¹², 16131, F₆₄, 5) (dual of [16131, 16119, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(64¹², 16132, F₆₄, 5) (dual of [16132, 16120, 6]-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OA(64¹, 4033, F₆₄, 1) (dual of [4033, 4032, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OA(64¹, 4033, F₆₄, 1) (dual of [4033, 4032, 2]-code) (see above)
    3. linear OA(64³, 4033, F₆₄, 2) (dual of [4033, 4030, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
        Hamming code H(3,64) [i]
    4. linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 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, 1685785)-net over F₆₄	[i]		(u,Â u+v)-Construction for Nets
2	Digital (42, 53, 1685785)-net over F₆₄	[i]		(u,Â u+v)-Construction for Nets