MinT - Information on Result #1157536

Information on Result #1157536

Linear OOA(2¹⁴⁸, 66, F₂, 7, 59) (dual of [(66, 7), 314, 60]-NRT-code), using extracting embedded OOA based on digital (89, 148, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 74, 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(2¹⁴⁸, 66, F₂, 7, 58) (dual of [(66, 7), 314, 59]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁴⁸, 66, F₂, 7, 57) (dual of [(66, 7), 314, 58]-NRT-code)	[i]
3	Linear OOA(2¹⁴⁸, 66, F₂, 7, 56) (dual of [(66, 7), 314, 57]-NRT-code)	[i]
4	Linear OOA(2¹⁵⁵, 67, F₂, 7, 59) (dual of [(67, 7), 314, 60]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
5	Linear OOA(2¹⁴⁹, 66, F₂, 7, 59) (dual of [(66, 7), 313, 60]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2¹⁵¹, 66, F₂, 7, 59) (dual of [(66, 7), 311, 60]-NRT-code)	[i]
7	Linear OOA(2¹⁵³, 66, F₂, 7, 59) (dual of [(66, 7), 309, 60]-NRT-code)	[i]
8	Linear OOA(2¹⁷⁸, 71, F₂, 7, 59) (dual of [(71, 7), 319, 60]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
9	Linear OOA(2¹⁸⁰, 73, F₂, 7, 59) (dual of [(73, 7), 331, 60]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs