MinT - Information on Result #1188196

Information on Result #1188196

Digital (12, 19, 124)-net over F₅, using net defined by OOA based on linear OOA(5¹⁹, 124, F₅, 9, 7) (dual of [(124, 9), 1097, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(5¹⁹, 125, F₅, 3, 7) (dual of [(125, 3), 356, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹, 25, F₅, 3, 1) (dual of [(25, 3), 74, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5¹, s, F₅, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(5¹, 25, F₅, 3, 1) (dual of [(25, 3), 74, 2]-NRT-code) (see above)
  3. linear OOA(5³, 25, F₅, 3, 2) (dual of [(25, 3), 72, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5³, 31, F₅, 3, 2) (dual of [(31, 3), 90, 3]-NRT-code), using
      - appending 1 arbitrary column [i] based on linear OOA(5³, 31, F₅, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
        appending kth column [i] based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
        Hamming code H(3,5) [i]
  4. linear OOA(5⁴, 25, F₅, 3, 3) (dual of [(25, 3), 71, 4]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OA(5⁴, 26, F₅, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
      - ovoid in PG(3,Â 5) [i]
  5. linear OOA(5¹⁰, 25, F₅, 3, 7) (dual of [(25, 3), 65, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 10, 25)-net over F₅, 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 (41, 55, 256)-net over F₅	[i]	(u,Â u+v)-Construction for Nets
2	Digital (116, 130, 1198495)-net over F₅	[i]
3	Digital (42, 57, 256)-net over F₅	[i]
4	Digital (124, 139, 1198495)-net over F₅	[i]