MinT - Information on Result #1000450

Information on Result #1000450

Linear OOA(2⁷², 42, F₂, 3, 29) (dual of [(42, 3), 54, 30]-NRT-code), using extracting embedded OOA based on digital (43, 72, 42)-net over F₂, using

trace code for nets [i] based on digital (7, 36, 21)-net over F₄, using
- net from sequence [i] based on digital (7, 20)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [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(2⁷², 42, F₂, 3, 28) (dual of [(42, 3), 54, 29]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2⁷⁵, 43, F₂, 3, 29) (dual of [(43, 3), 54, 30]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(2⁷³, 42, F₂, 3, 29) (dual of [(42, 3), 53, 30]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(2¹⁷⁹, 80, F₂, 3, 58) (dual of [(80, 3), 61, 59]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
5	Linear OOA(2¹⁷⁹, 80, F₂, 3, 59) (dual of [(80, 3), 61, 60]-NRT-code)	[i]
6	Linear OOA(2¹⁸², 82, F₂, 3, 59) (dual of [(82, 3), 64, 60]-NRT-code)	[i]
7	Linear OOA(2⁷², 21, F₂, 5, 29) (dual of [(21, 5), 33, 30]-NRT-code)	[i]		OOA Folding
8	Linear OOA(2⁷², 21, F₂, 6, 29) (dual of [(21, 6), 54, 30]-NRT-code)	[i]		OOA Folding