MinT - Information on Result #1076746

Information on Result #1076746

Linear OOA(3¹⁵⁸, 156, F₃, 4, 57) (dual of [(156, 4), 466, 58]-NRT-code), using extracting embedded OOA based on digital (101, 158, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 79, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [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(3¹⁵⁸, 156, F₃, 4, 56) (dual of [(156, 4), 466, 57]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁶², 157, F₃, 4, 57) (dual of [(157, 4), 466, 58]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(3¹⁶⁶, 158, F₃, 4, 57) (dual of [(158, 4), 466, 58]-NRT-code)	[i]
4	Linear OOA(3¹⁷⁰, 159, F₃, 4, 57) (dual of [(159, 4), 466, 58]-NRT-code)	[i]
5	Linear OOA(3¹⁷⁴, 160, F₃, 4, 57) (dual of [(160, 4), 466, 58]-NRT-code)	[i]
6	Linear OOA(3¹⁵⁹, 156, F₃, 4, 57) (dual of [(156, 4), 465, 58]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(3¹⁶¹, 156, F₃, 4, 57) (dual of [(156, 4), 463, 58]-NRT-code)	[i]		OOA Duplication