MinT - Information on Result #1157311

Information on Result #1157311

Linear OOA(2¹³⁰, 66, F₂, 7, 50) (dual of [(66, 7), 332, 51]-NRT-code), using extracting embedded OOA based on digital (80, 130, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 65, 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(2¹³⁰, 66, F₂, 7, 49) (dual of [(66, 7), 332, 50]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹³⁰, 66, F₂, 7, 48) (dual of [(66, 7), 332, 49]-NRT-code)	[i]
3	Linear OOA(2¹³⁰, 66, F₂, 7, 47) (dual of [(66, 7), 332, 48]-NRT-code)	[i]
4	Linear OOA(2¹³⁷, 67, F₂, 7, 50) (dual of [(67, 7), 332, 51]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
5	Linear OOA(2¹³¹, 66, F₂, 7, 50) (dual of [(66, 7), 331, 51]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2¹³³, 66, F₂, 7, 50) (dual of [(66, 7), 329, 51]-NRT-code)	[i]
7	Linear OOA(2¹³⁵, 66, F₂, 7, 50) (dual of [(66, 7), 327, 51]-NRT-code)	[i]
8	Linear OOA(2¹⁵⁶, 71, F₂, 7, 50) (dual of [(71, 7), 341, 51]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
9	Linear OOA(2¹⁵⁷, 72, F₂, 7, 50) (dual of [(72, 7), 347, 51]-NRT-code)	[i]
10	Linear OOA(2¹⁵⁸, 73, F₂, 7, 50) (dual of [(73, 7), 353, 51]-NRT-code)	[i]
11	Linear OOA(2¹⁵⁹, 74, F₂, 7, 50) (dual of [(74, 7), 359, 51]-NRT-code)	[i]
12	Linear OOA(2¹⁶⁰, 75, F₂, 7, 50) (dual of [(75, 7), 365, 51]-NRT-code)	[i]
13	Linear OOA(2¹⁶¹, 76, F₂, 7, 50) (dual of [(76, 7), 371, 51]-NRT-code)	[i]
14	Linear OOA(2¹⁶³, 77, F₂, 7, 50) (dual of [(77, 7), 376, 51]-NRT-code)	[i]
15	Linear OOA(2¹⁶⁴, 78, F₂, 7, 50) (dual of [(78, 7), 382, 51]-NRT-code)	[i]