MinT - Information on Result #1075471

Information on Result #1075471

Linear OOA(2²¹⁸, 112, F₂, 4, 76) (dual of [(112, 4), 230, 77]-NRT-code), using extracting embedded OOA based on digital (142, 218, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 109, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [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(2²¹⁸, 112, F₂, 4, 75) (dual of [(112, 4), 230, 76]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²²², 113, F₂, 4, 76) (dual of [(113, 4), 230, 77]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(2²²⁶, 114, F₂, 4, 76) (dual of [(114, 4), 230, 77]-NRT-code)	[i]
4	Linear OOA(2²³⁰, 115, F₂, 4, 76) (dual of [(115, 4), 230, 77]-NRT-code)	[i]
5	Linear OOA(2²³⁴, 116, F₂, 4, 76) (dual of [(116, 4), 230, 77]-NRT-code)	[i]
6	Linear OOA(2²³⁸, 117, F₂, 4, 76) (dual of [(117, 4), 230, 77]-NRT-code)	[i]
7	Linear OOA(2²⁴², 118, F₂, 4, 76) (dual of [(118, 4), 230, 77]-NRT-code)	[i]
8	Linear OOA(2²⁴⁶, 119, F₂, 4, 76) (dual of [(119, 4), 230, 77]-NRT-code)	[i]
9	Linear OOA(2²¹⁹, 112, F₂, 4, 76) (dual of [(112, 4), 229, 77]-NRT-code)	[i]		OOA Duplication
10	Linear OOA(2²²¹, 112, F₂, 4, 76) (dual of [(112, 4), 227, 77]-NRT-code)	[i]		OOA Duplication
11	Linear OOA(2²¹⁸, 56, F₂, 7, 76) (dual of [(56, 7), 174, 77]-NRT-code)	[i]		OOA Folding
12	Linear OOA(2²¹⁸, 56, F₂, 8, 76) (dual of [(56, 8), 230, 77]-NRT-code)	[i]		OOA Folding