MinT - Information on Result #1173349

Information on Result #1173349

Linear OOA(2¹⁴², 66, F₂, 8, 56) (dual of [(66, 8), 386, 57]-NRT-code), using extracting embedded OOA based on digital (86, 142, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 71, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, 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(2¹⁴², 66, F₂, 8, 55) (dual of [(66, 8), 386, 56]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁴², 66, F₂, 8, 54) (dual of [(66, 8), 386, 55]-NRT-code)	[i]
3	Linear OOA(2¹⁴², 66, F₂, 8, 53) (dual of [(66, 8), 386, 54]-NRT-code)	[i]
4	Linear OOA(2¹⁵⁰, 67, F₂, 8, 56) (dual of [(67, 8), 386, 57]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
5	Linear OOA(2¹⁴³, 66, F₂, 8, 56) (dual of [(66, 8), 385, 57]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2¹⁴⁵, 66, F₂, 8, 56) (dual of [(66, 8), 383, 57]-NRT-code)	[i]
7	Linear OOA(2¹⁴⁷, 66, F₂, 8, 56) (dual of [(66, 8), 381, 57]-NRT-code)	[i]
8	Linear OOA(2¹⁴⁹, 66, F₂, 8, 56) (dual of [(66, 8), 379, 57]-NRT-code)	[i]
9	Linear OOA(2¹⁷¹, 71, F₂, 8, 56) (dual of [(71, 8), 397, 57]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
10	Linear OOA(2¹⁷², 72, F₂, 8, 56) (dual of [(72, 8), 404, 57]-NRT-code)	[i]
11	Linear OOA(2¹⁷³, 73, F₂, 8, 56) (dual of [(73, 8), 411, 57]-NRT-code)	[i]
12	Linear OOA(2¹⁷⁴, 74, F₂, 8, 56) (dual of [(74, 8), 418, 57]-NRT-code)	[i]
13	Linear OOA(2¹⁷⁵, 75, F₂, 8, 56) (dual of [(75, 8), 425, 57]-NRT-code)	[i]