MinT - Information on Result #1077551

Information on Result #1077551

Linear OOA(3²⁰⁸, 688, F₃, 4, 45) (dual of [(688, 4), 2544, 46]-NRT-code), using extracting embedded OOA based on digital (163, 208, 688)-net over F₃, using

trace code for nets [i] based on digital (7, 52, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [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(3²¹², 689, F₃, 4, 45) (dual of [(689, 4), 2544, 46]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(3²¹⁶, 690, F₃, 4, 45) (dual of [(690, 4), 2544, 46]-NRT-code)	[i]
3	Linear OOA(3²²⁰, 691, F₃, 4, 45) (dual of [(691, 4), 2544, 46]-NRT-code)	[i]
4	Linear OOA(3²²⁴, 692, F₃, 4, 45) (dual of [(692, 4), 2544, 46]-NRT-code)	[i]
5	Linear OOA(3²²⁸, 693, F₃, 4, 45) (dual of [(693, 4), 2544, 46]-NRT-code)	[i]
6	Linear OOA(3²⁰⁹, 688, F₃, 4, 45) (dual of [(688, 4), 2543, 46]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(3²¹⁰, 688, F₃, 4, 45) (dual of [(688, 4), 2542, 46]-NRT-code)	[i]
8	Linear OOA(3²¹¹, 688, F₃, 4, 45) (dual of [(688, 4), 2541, 46]-NRT-code)	[i]
9	Linear OOA(3²³¹, 695, F₃, 4, 45) (dual of [(695, 4), 2549, 46]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs