MinT - Information on Result #1178947

Information on Result #1178947

Digital (12, 17, 231)-net over F₃, using net defined by OOA based on linear OOA(3¹⁷, 231, F₃, 5, 5) (dual of [(231, 5), 1138, 6]-NRT-code), using

appending kth column [i] based on linear OOA(3¹⁷, 231, F₃, 4, 5) (dual of [(231, 4), 907, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹, 77, F₃, 4, 1) (dual of [(77, 4), 307, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 4, 1) for arbitrarily large s, using
      - appending 3 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(3⁵, 77, F₃, 4, 2) (dual of [(77, 4), 303, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁵, 121, F₃, 4, 2) (dual of [(121, 4), 479, 3]-NRT-code), using
      - appending 2 arbitrary columns [i] based on linear OOA(3⁵, 121, F₃, 2, 2) (dual of [(121, 2), 237, 3]-NRT-code), using
        appending kth column [i] based on linear OA(3⁵, 121, F₃, 2) (dual of [121, 116, 3]-code), using
        Hamming code H(5,3) [i]
  3. linear OOA(3¹¹, 77, F₃, 4, 5) (dual of [(77, 4), 297, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 11, 77)-net over F₃, 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		This result only	Method
1	Digital (98, 108, 1677951)-net over F₃	[i]		(u,Â u+v)-Construction for Nets
2	Digital (155, 165, 6711111)-net over F₃	[i]
3	Digital (112, 123, 1677951)-net over F₃	[i]
4	Digital (170, 181, 6711111)-net over F₃	[i]