MinT - Information on Result #1003415

Information on Result #1003415

Linear OOA(4¹⁷¹, 531, F₄, 3, 50) (dual of [(531, 3), 1422, 51]-NRT-code), using extracting embedded OOA based on digital (121, 171, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 57, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [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(4¹⁷⁴, 532, F₄, 3, 50) (dual of [(532, 3), 1422, 51]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(4¹⁷⁷, 533, F₄, 3, 50) (dual of [(533, 3), 1422, 51]-NRT-code)	[i]
3	Linear OOA(4¹⁸⁰, 534, F₄, 3, 50) (dual of [(534, 3), 1422, 51]-NRT-code)	[i]
4	Linear OOA(4¹⁷², 531, F₄, 3, 50) (dual of [(531, 3), 1421, 51]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(4¹⁷³, 531, F₄, 3, 50) (dual of [(531, 3), 1420, 51]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(4¹⁹⁷, 540, F₄, 3, 50) (dual of [(540, 3), 1423, 51]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
7	Linear OOA(4¹⁹⁸, 541, F₄, 3, 50) (dual of [(541, 3), 1425, 51]-NRT-code)	[i]
8	Linear OOA(4¹⁹⁹, 545, F₄, 3, 50) (dual of [(545, 3), 1436, 51]-NRT-code)	[i]