MinT - Information on Result #2642811

Information on Result #2642811

Linear OOA(7¹⁰⁹, 45, F₇, 3, 67) (dual of [(45, 3), 26, 68]-NRT-code), using strength reduction based on linear OOA(7¹⁰⁹, 45, F₇, 3, 68) (dual of [(45, 3), 26, 69]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7¹⁴, 9, F₇, 3, 13) (dual of [(9, 3), 13, 14]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 14, 9)-net over F₇, using
    - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
      - Niederreiter sequence [i]
2. linear OOA(7¹⁸, 9, F₇, 3, 17) (dual of [(9, 3), 9, 18]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 18, 9)-net over F₇, using
    - net from sequence [i] based on digital (1, 8)-sequence over F₇ (see above)
3. linear OOA(7²³, 9, F₇, 3, 22) (dual of [(9, 3), 4, 23]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 23, 9)-net over F₇, using
    - net from sequence [i] based on digital (1, 8)-sequence over F₇ (see above)
4. linear OOA(7²⁷, 9, F₇, 3, 27) (dual of [(9, 3), 0, 28]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
5. linear OOA(7²⁷, 9, F₇, 3, 27) (dual of [(9, 3), 0, 28]-NRT-code) (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.