MinT - Information on Result #1113705

Information on Result #1113705

Linear OOA(3²²⁶, 162, F₃, 5, 81) (dual of [(162, 5), 584, 82]-NRT-code), using extracting embedded OOA based on digital (145, 226, 162)-net over F₃, using

trace code for nets [i] based on digital (32, 113, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa 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(3²²⁶, 162, F₃, 5, 80) (dual of [(162, 5), 584, 81]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²²⁶, 162, F₃, 5, 79) (dual of [(162, 5), 584, 80]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²³¹, 163, F₃, 5, 81) (dual of [(163, 5), 584, 82]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(3²³⁶, 164, F₃, 5, 81) (dual of [(164, 5), 584, 82]-NRT-code)	[i]
5	Linear OOA(3²⁴¹, 165, F₃, 5, 81) (dual of [(165, 5), 584, 82]-NRT-code)	[i]
6	Linear OOA(3²²⁷, 162, F₃, 5, 81) (dual of [(162, 5), 583, 82]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(3²²⁹, 162, F₃, 5, 81) (dual of [(162, 5), 581, 82]-NRT-code)	[i]		OOA Duplication