MinT - Information on Result #1112819

Information on Result #1112819

Linear OOA(3¹⁸⁸, 156, F₃, 5, 72) (dual of [(156, 5), 592, 73]-NRT-code), using extracting embedded OOA based on digital (116, 188, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 94, 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(3¹⁸⁸, 156, F₃, 5, 71) (dual of [(156, 5), 592, 72]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁸⁸, 156, F₃, 5, 70) (dual of [(156, 5), 592, 71]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁹³, 157, F₃, 5, 72) (dual of [(157, 5), 592, 73]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(3¹⁹⁸, 158, F₃, 5, 72) (dual of [(158, 5), 592, 73]-NRT-code)	[i]
5	Linear OOA(3²⁰³, 159, F₃, 5, 72) (dual of [(159, 5), 592, 73]-NRT-code)	[i]
6	Linear OOA(3¹⁸⁹, 156, F₃, 5, 72) (dual of [(156, 5), 591, 73]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(3¹⁹¹, 156, F₃, 5, 72) (dual of [(156, 5), 589, 73]-NRT-code)	[i]		OOA Duplication