MinT - Information on Result #1157428

Information on Result #1157428

Linear OOA(2¹⁴⁰, 66, F₂, 7, 55) (dual of [(66, 7), 322, 56]-NRT-code), using extracting embedded OOA based on digital (85, 140, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 70, 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(2¹⁴⁰, 66, F₂, 7, 54) (dual of [(66, 7), 322, 55]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁴⁰, 66, F₂, 7, 53) (dual of [(66, 7), 322, 54]-NRT-code)	[i]
3	Linear OOA(2¹⁴⁰, 66, F₂, 7, 52) (dual of [(66, 7), 322, 53]-NRT-code)	[i]
4	Linear OOA(2¹⁴⁷, 67, F₂, 7, 55) (dual of [(67, 7), 322, 56]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
5	Linear OOA(2¹⁴¹, 66, F₂, 7, 55) (dual of [(66, 7), 321, 56]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2¹⁴³, 66, F₂, 7, 55) (dual of [(66, 7), 319, 56]-NRT-code)	[i]
7	Linear OOA(2¹⁴⁵, 66, F₂, 7, 55) (dual of [(66, 7), 317, 56]-NRT-code)	[i]
8	Linear OOA(2¹⁶⁸, 71, F₂, 7, 55) (dual of [(71, 7), 329, 56]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
9	Linear OOA(2¹⁶⁹, 72, F₂, 7, 55) (dual of [(72, 7), 335, 56]-NRT-code)	[i]
10	Linear OOA(2¹⁷⁰, 73, F₂, 7, 55) (dual of [(73, 7), 341, 56]-NRT-code)	[i]
11	Linear OOA(2¹⁷¹, 74, F₂, 7, 55) (dual of [(74, 7), 347, 56]-NRT-code)	[i]
12	Linear OOA(2¹⁷², 75, F₂, 7, 55) (dual of [(75, 7), 353, 56]-NRT-code)	[i]
13	Linear OOA(2¹⁷⁵, 77, F₂, 7, 55) (dual of [(77, 7), 364, 56]-NRT-code)	[i]