MinT - Information on Result #1157817

Information on Result #1157817

Linear OOA(2¹⁶⁸, 66, F₂, 7, 69) (dual of [(66, 7), 294, 70]-NRT-code), using extracting embedded OOA based on digital (99, 168, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 84, 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(2¹⁶⁸, 66, F₂, 7, 68) (dual of [(66, 7), 294, 69]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁶⁸, 66, F₂, 7, 67) (dual of [(66, 7), 294, 68]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁸, 66, F₂, 7, 66) (dual of [(66, 7), 294, 67]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁵, 67, F₂, 7, 69) (dual of [(67, 7), 294, 70]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
5	Linear OOA(2¹⁶⁹, 66, F₂, 7, 69) (dual of [(66, 7), 293, 70]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2¹⁷¹, 66, F₂, 7, 69) (dual of [(66, 7), 291, 70]-NRT-code)	[i]
7	Linear OOA(2¹⁷³, 66, F₂, 7, 69) (dual of [(66, 7), 289, 70]-NRT-code)	[i]