MinT - Information on Result #1185820

Information on Result #1185820

Digital (12, 19, 70)-net over F₄, using net defined by OOA based on linear OOA(4¹⁹, 70, F₄, 9, 7) (dual of [(70, 9), 611, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(4¹⁹, 71, F₄, 3, 7) (dual of [(71, 3), 194, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹, 17, F₄, 3, 1) (dual of [(17, 3), 50, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹, s, F₄, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(4³, 17, F₄, 3, 2) (dual of [(17, 3), 48, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4³, 21, F₄, 3, 2) (dual of [(21, 3), 60, 3]-NRT-code), using
      - appending 1 arbitrary column [i] based on linear OOA(4³, 21, F₄, 2, 2) (dual of [(21, 2), 39, 3]-NRT-code), using
        appending kth column [i] based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
        Hamming code H(3,4) [i]
  3. linear OOA(4⁴, 17, F₄, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(4⁴, 17, F₄, 2, 3) (dual of [(17, 2), 30, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
        ovoid in PG(3,Â 4) [i]
  4. linear OOA(4¹¹, 20, F₄, 3, 7) (dual of [(20, 3), 49, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 11, 20)-net over F₄, using
      - linear code embedding found in a computer search [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 (126, 140, 1198441)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
2	Digital (165, 179, 4793554)-net over F₄	[i]
3	Digital (137, 152, 1198441)-net over F₄	[i]
4	Digital (176, 191, 4793554)-net over F₄	[i]