MinT - Information on Result #1113269

Information on Result #1113269

Linear OOA(3²⁰⁸, 688, F₃, 5, 45) (dual of [(688, 5), 3232, 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(3²⁰⁸, 688, F₃, 5, 44) (dual of [(688, 5), 3232, 45]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²¹³, 689, F₃, 5, 45) (dual of [(689, 5), 3232, 46]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(3²¹⁸, 690, F₃, 5, 45) (dual of [(690, 5), 3232, 46]-NRT-code)	[i]
4	Linear OOA(3²²³, 691, F₃, 5, 45) (dual of [(691, 5), 3232, 46]-NRT-code)	[i]
5	Linear OOA(3²²⁸, 692, F₃, 5, 45) (dual of [(692, 5), 3232, 46]-NRT-code)	[i]
6	Linear OOA(3²⁰⁹, 688, F₃, 5, 45) (dual of [(688, 5), 3231, 46]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(3²¹⁰, 688, F₃, 5, 45) (dual of [(688, 5), 3230, 46]-NRT-code)	[i]
8	Linear OOA(3²¹¹, 688, F₃, 5, 45) (dual of [(688, 5), 3229, 46]-NRT-code)	[i]
9	Linear OOA(3²³¹, 695, F₃, 5, 45) (dual of [(695, 5), 3244, 46]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs