MinT - Information on Result #1157673

Information on Result #1157673

Linear OOA(2¹⁵⁸, 66, F₂, 7, 64) (dual of [(66, 7), 304, 65]-NRT-code), using extracting embedded OOA based on digital (94, 158, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 79, 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(2¹⁵⁸, 66, F₂, 7, 63) (dual of [(66, 7), 304, 64]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁵⁸, 66, F₂, 7, 62) (dual of [(66, 7), 304, 63]-NRT-code)	[i]
3	Linear OOA(2¹⁵⁸, 66, F₂, 7, 61) (dual of [(66, 7), 304, 62]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁵, 67, F₂, 7, 64) (dual of [(67, 7), 304, 65]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
5	Linear OOA(2¹⁵⁹, 66, F₂, 7, 64) (dual of [(66, 7), 303, 65]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2¹⁶¹, 66, F₂, 7, 64) (dual of [(66, 7), 301, 65]-NRT-code)	[i]
7	Linear OOA(2¹⁶³, 66, F₂, 7, 64) (dual of [(66, 7), 299, 65]-NRT-code)	[i]