MinT - Information on Result #1003427

Information on Result #1003427

Linear OOA(4¹⁷⁴, 531, F₄, 3, 51) (dual of [(531, 3), 1419, 52]-NRT-code), using extracting embedded OOA based on digital (123, 174, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 58, 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(4¹⁷⁷, 532, F₄, 3, 51) (dual of [(532, 3), 1419, 52]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(4¹⁸⁰, 533, F₄, 3, 51) (dual of [(533, 3), 1419, 52]-NRT-code)	[i]
3	Linear OOA(4¹⁸³, 534, F₄, 3, 51) (dual of [(534, 3), 1419, 52]-NRT-code)	[i]
4	Linear OOA(4¹⁷⁵, 531, F₄, 3, 51) (dual of [(531, 3), 1418, 52]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(4¹⁷⁶, 531, F₄, 3, 51) (dual of [(531, 3), 1417, 52]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(4²⁰⁰, 540, F₄, 3, 51) (dual of [(540, 3), 1420, 52]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
7	Linear OOA(4²⁰¹, 541, F₄, 3, 51) (dual of [(541, 3), 1422, 52]-NRT-code)	[i]
8	Linear OOA(4²⁰², 545, F₄, 3, 51) (dual of [(545, 3), 1433, 52]-NRT-code)	[i]
9	Linear OOA(4²⁰³, 546, F₄, 3, 51) (dual of [(546, 3), 1435, 52]-NRT-code)	[i]