MinT - Information on Result #1015137

Information on Result #1015137

Linear OOA(8¹⁰⁶, 484, F₈, 3, 31) (dual of [(484, 3), 1346, 32]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8³⁰, 130, F₈, 3, 15) (dual of [(130, 3), 360, 16]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 30, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 15, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
linear OOA(8⁷⁶, 354, F₈, 3, 31) (dual of [(354, 3), 986, 32]-NRT-code), using
- extracting embedded OOA [i] based on digital (45, 76, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 38, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [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(8¹⁰⁷, 484, F₈, 3, 31) (dual of [(484, 3), 1345, 32]-NRT-code)	[i]		OOA Duplication