MinT - Information on Result #1075186

Information on Result #1075186

Linear OOA(2¹⁴⁸, 66, F₂, 4, 59) (dual of [(66, 4), 116, 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, 4, 58) (dual of [(66, 4), 116, 59]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁵², 67, F₂, 4, 59) (dual of [(67, 4), 116, 60]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(2¹⁵⁶, 68, F₂, 4, 59) (dual of [(68, 4), 116, 60]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁰, 69, F₂, 4, 59) (dual of [(69, 4), 116, 60]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁴, 70, F₂, 4, 59) (dual of [(70, 4), 116, 60]-NRT-code)	[i]
6	Linear OOA(2¹⁶⁸, 71, F₂, 4, 59) (dual of [(71, 4), 116, 60]-NRT-code)	[i]
7	Linear OOA(2¹⁷², 72, F₂, 4, 59) (dual of [(72, 4), 116, 60]-NRT-code)	[i]
8	Linear OOA(2¹⁷⁶, 73, F₂, 4, 59) (dual of [(73, 4), 116, 60]-NRT-code)	[i]
9	Linear OOA(2¹⁴⁹, 66, F₂, 4, 59) (dual of [(66, 4), 115, 60]-NRT-code)	[i]		OOA Duplication
10	Linear OOA(2¹⁵¹, 66, F₂, 4, 59) (dual of [(66, 4), 113, 60]-NRT-code)	[i]		OOA Duplication
11	Linear OOA(2¹⁷⁹, 74, F₂, 4, 59) (dual of [(74, 4), 117, 60]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
12	Linear OOA(2¹⁴⁸, 33, F₂, 7, 59) (dual of [(33, 7), 83, 60]-NRT-code)	[i]		OOA Folding
13	Linear OOA(2¹⁴⁸, 33, F₂, 8, 59) (dual of [(33, 8), 116, 60]-NRT-code)	[i]		OOA Folding