MinT - Information on Result #1075415

Information on Result #1075415

Linear OOA(2¹⁹⁸, 112, F₂, 4, 66) (dual of [(112, 4), 250, 67]-NRT-code), using extracting embedded OOA based on digital (132, 198, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 99, 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(2¹⁹⁸, 112, F₂, 4, 65) (dual of [(112, 4), 250, 66]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁰², 113, F₂, 4, 66) (dual of [(113, 4), 250, 67]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
3	Linear OOA(2²⁰⁶, 114, F₂, 4, 66) (dual of [(114, 4), 250, 67]-NRT-code)	[i]
4	Linear OOA(2²¹⁰, 115, F₂, 4, 66) (dual of [(115, 4), 250, 67]-NRT-code)	[i]
5	Linear OOA(2²¹⁴, 116, F₂, 4, 66) (dual of [(116, 4), 250, 67]-NRT-code)	[i]
6	Linear OOA(2²¹⁸, 117, F₂, 4, 66) (dual of [(117, 4), 250, 67]-NRT-code)	[i]
7	Linear OOA(2²²², 118, F₂, 4, 66) (dual of [(118, 4), 250, 67]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁹, 112, F₂, 4, 66) (dual of [(112, 4), 249, 67]-NRT-code)	[i]		OOA Duplication
9	Linear OOA(2²⁰¹, 112, F₂, 4, 66) (dual of [(112, 4), 247, 67]-NRT-code)	[i]		OOA Duplication
10	Linear OOA(2¹⁹⁸, 56, F₂, 7, 66) (dual of [(56, 7), 194, 67]-NRT-code)	[i]		OOA Folding
11	Linear OOA(2¹⁹⁸, 56, F₂, 8, 66) (dual of [(56, 8), 250, 67]-NRT-code)	[i]		OOA Folding