MinT - Information on Result #1140872

Information on Result #1140872

Linear OOA(2¹⁶⁶, 112, F₂, 6, 50) (dual of [(112, 6), 506, 51]-NRT-code), using extracting embedded OOA based on digital (116, 166, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 83, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [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(2¹⁶⁶, 112, F₂, 6, 49) (dual of [(112, 6), 506, 50]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁶⁶, 112, F₂, 6, 48) (dual of [(112, 6), 506, 49]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2¹⁷², 113, F₂, 6, 50) (dual of [(113, 6), 506, 51]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(2¹⁶⁷, 112, F₂, 6, 50) (dual of [(112, 6), 505, 51]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(2¹⁶⁹, 112, F₂, 6, 50) (dual of [(112, 6), 503, 51]-NRT-code)	[i]
6	Linear OOA(2¹⁷¹, 112, F₂, 6, 50) (dual of [(112, 6), 501, 51]-NRT-code)	[i]