MinT - Information on Result #1112175

Information on Result #1112175

Linear OOA(3¹⁴², 156, F₃, 5, 49) (dual of [(156, 5), 638, 50]-NRT-code), using extracting embedded OOA based on digital (93, 142, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 71, 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(3¹⁴², 156, F₃, 5, 48) (dual of [(156, 5), 638, 49]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁴², 156, F₃, 5, 47) (dual of [(156, 5), 638, 48]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁴⁷, 157, F₃, 5, 49) (dual of [(157, 5), 638, 50]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(3¹⁵², 158, F₃, 5, 49) (dual of [(158, 5), 638, 50]-NRT-code)	[i]
5	Linear OOA(3¹⁵⁷, 159, F₃, 5, 49) (dual of [(159, 5), 638, 50]-NRT-code)	[i]
6	Linear OOA(3¹⁴³, 156, F₃, 5, 49) (dual of [(156, 5), 637, 50]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(3¹⁴⁵, 156, F₃, 5, 49) (dual of [(156, 5), 635, 50]-NRT-code)	[i]		OOA Duplication