MinT - Information on Result #1170701

Information on Result #1170701

Linear OOA(2³², 78, F₂, 8, 8) (dual of [(78, 8), 592, 9]-NRT-code), using appending kth column based on linear OOA(2³², 78, F₂, 7, 8) (dual of [(78, 7), 514, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹¹, 47, F₂, 7, 4) (dual of [(47, 7), 318, 5]-NRT-code), using
  - appending 3 arbitrary columns [i] based on linear OOA(2¹¹, 47, F₂, 4, 4) (dual of [(47, 4), 177, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹¹, 47, F₂, 3, 4) (dual of [(47, 3), 130, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [i]
2. linear OOA(2²¹, 39, F₂, 7, 8) (dual of [(39, 7), 252, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (13, 21, 39)-net over F₂, using
    - linear code embedding found in a computer search [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		Method
1	Linear OOA(2³³, 78, F₂, 8, 8) (dual of [(78, 8), 591, 9]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2³⁴, 78, F₂, 8, 8) (dual of [(78, 8), 590, 9]-NRT-code)	[i]
3	Linear OOA(2³⁵, 78, F₂, 8, 8) (dual of [(78, 8), 589, 9]-NRT-code)	[i]
4	Linear OOA(2²¹⁶, 1048653, F₂, 8, 16) (dual of [(1048653, 8), 8389008, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
5	Linear OOA(2²¹⁷, 1048653, F₂, 8, 17) (dual of [(1048653, 8), 8389007, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
6	Digital (24, 32, 78)-net over F₂	[i]	Net Defined by OOA