MinT - Information on Result #2805333

Information on Result #2805333

Linear OOA(3¹⁹¹, 75, F₃, 4, 89) (dual of [(75, 4), 109, 90]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3¹⁸⁷, 74, F₃, 4, 89) (dual of [(74, 4), 109, 90]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁷¹, 37, F₃, 4, 44) (dual of [(37, 4), 77, 45]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 71, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. linear OOA(3¹¹⁶, 37, F₃, 4, 89) (dual of [(37, 4), 32, 90]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 116, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁹², 75, F₃, 4, 89) (dual of [(75, 4), 108, 90]-NRT-code)	[i]		OOA Duplication