MinT - Information on Result #1140371

Information on Result #1140371

Linear OOA(2¹²², 66, F₂, 6, 46) (dual of [(66, 6), 274, 47]-NRT-code), using extracting embedded OOA based on digital (76, 122, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 61, 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(2¹²², 66, F₂, 6, 45) (dual of [(66, 6), 274, 46]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹²², 66, F₂, 6, 44) (dual of [(66, 6), 274, 45]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2¹²⁸, 67, F₂, 6, 46) (dual of [(67, 6), 274, 47]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(2¹³⁴, 68, F₂, 6, 46) (dual of [(68, 6), 274, 47]-NRT-code)	[i]
5	Linear OOA(2¹⁴⁰, 69, F₂, 6, 46) (dual of [(69, 6), 274, 47]-NRT-code)	[i]
6	Linear OOA(2¹²³, 66, F₂, 6, 46) (dual of [(66, 6), 273, 47]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(2¹²⁵, 66, F₂, 6, 46) (dual of [(66, 6), 271, 47]-NRT-code)	[i]
8	Linear OOA(2¹²⁷, 66, F₂, 6, 46) (dual of [(66, 6), 269, 47]-NRT-code)	[i]
9	Linear OOA(2¹⁴⁵, 70, F₂, 6, 46) (dual of [(70, 6), 275, 47]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
10	Linear OOA(2¹⁴⁶, 71, F₂, 6, 46) (dual of [(71, 6), 280, 47]-NRT-code)	[i]
11	Linear OOA(2¹⁴⁸, 73, F₂, 6, 46) (dual of [(73, 6), 290, 47]-NRT-code)	[i]
12	Linear OOA(2¹⁴⁹, 74, F₂, 6, 46) (dual of [(74, 6), 295, 47]-NRT-code)	[i]
13	Linear OOA(2¹⁵¹, 76, F₂, 6, 46) (dual of [(76, 6), 305, 47]-NRT-code)	[i]