MinT - Information on Result #1014055

Information on Result #1014055

Linear OOA(7⁵⁷, 126, F₇, 3, 20) (dual of [(126, 3), 321, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹⁷, 26, F₇, 3, 10) (dual of [(26, 3), 61, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁶, 13, F₇, 3, 5) (dual of [(13, 3), 33, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 6, 13)-net over F₇, using
      - 7 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
  2. linear OOA(7¹¹, 13, F₇, 3, 10) (dual of [(13, 3), 28, 11]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 11, 13)-net over F₇, using
      - 2 times m-reduction [i] based on digital (1, 13, 13)-net over F₇ (see above)
linear OOA(7⁴⁰, 100, F₇, 3, 20) (dual of [(100, 3), 260, 21]-NRT-code), using
- extracting embedded OOA [i] based on digital (20, 40, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 20, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
        the rational function field F₄₉(x) [i]
      - Niederreiter sequence [i]

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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁵⁸, 126, F₇, 3, 20) (dual of [(126, 3), 320, 21]-NRT-code)	[i]		OOA Duplication